Alright; I have seen graduate level seminars in World History run a couple different ways. One is focusing on a topic, be it environmental history, history of capitalism, maritime history, etc... and then reading through a historiographical evolution of the topic and looking at how World Historical perspectives provide the best answers to particular questions- or to put it another way- establishing what is a world historical question and how do you go about answering it. I've also seen it run as a sort of two parter- the first half focused on historiography of World History and the second half focused on World Historical research with the end goal of writing a solid research paper that might fit into a dissertation chapter or future article for publication.

Historiographically- or the materials covered by World History courses can very widely. Generally speaking, they might pick with with Marx or Von Ranke- or start a little later with Toynbee, Spengler, Stavrianos. Certainly you are likely to see Braudel in there- but I am not sure if anyone really assigns any of those authors to read, you can get most of their ideas from historiographical essays by later historians. Certainly you are likely to run into William McNeil, Alfred Crosby, Jerry Bentely, Kenneth Pommeranz, Immanuel Wallerstein, J.R. McNeil, Felipe Fernández-Armesto, Patrick Manning, Christopher Bayley, Prasannan Parthasarathi- and many more. I would say those guys are some of the highlights in the last twenty years.

To get a good overview of the field and maybe some understanding of what World Historians do (it doesn't usually involve writing the history of the world), I might check out some of the following if you have access:

• Allardyce, Gilbert. "Toward World History: American Historians and the Coming of the World History Course." Journal of World History 1, no. 1 (1990): 23-76.

• Pomeranz, Kenneth; Daniel A. Segal. "World History; Departures and Variations." In A Companion to World History, edited by Douglas Northrop. New York: Blackwell Publishing Ltd., 2012.

• Jerry H. Bentley, “The Task of World History” [sorry don't seem to have complete citation for this one handy...]

• Bentley, Jerry. "Sea and Ocean Basins as Frameworks of Historical Analysis." Geographical Review 89 (1999): 215-224.

As to the job opportunities... that totally depends on where you are! Many places use World History as the intro level course for undergraduate students- in fact all the universities near me do so; but this isn't the case everywhere. You could check out H-Net or the new H-net to see free job posting and get some idea of where places are hiring for World Historians. I believe- in the last job guide trend I saw- World Historian hiring had recovered decently, whereas American had not- so perhaps a good switch to make to find a job- but being able to teach both is even better.

Otherwise, being in California, depending on where you go there are a number of Big History folks kicking around, so thats another approach you might run into.

Not to be too gloom and doom- but the market for history professors in California is rough and anecdotally perhaps one of the toughest in the country. That said, who knows what it will be like when you are done! Yet, be prepared to move as you never know where the next great job opening will be.

For studying the Cold War in a global context, which is a wise move, you'll want a program that's not only strong in world but also US diplo/political. I went to a public Ivy program at a time when both were strong; we graduated a lot of top notch PhDs in the history of US foreign policy with a global or thematic focus. But the network of references and "friends of advisors" were in the old fields, and advertising was always for US first with world as a desired secondary. There's more demand for specifically world now; look at the listing, as /u/b1luepenguin points out among other wise advice.

However, one thing that we were told with no uncertainty is that world history can't stand on its own. It's a minor field, or an MA field, but you have to start from something somewhere. So our people were "US diplo 20th C. / Global-World-Comp" or something like that. Now, there's a fledgling MA program in world history in my old program that gears you that way from the get-go, but you still need to start somewhere and be in a place with your work. So you need not switch--you'll have major and minor fields. Just make sure to find the best people who can supervise you and are at a top-five program for that general field.

My global history background helped to get me my faculty job, as did my other fields--especially Africa, of course, where demand was highest for me relative to supply. All wanted me to be able to handle world surveys or global topics. So it is an essential component of successful candidacy these days, especially if you are doing anything that could possibly benefit from training in global, world, and/or comparative history. That said, the job market is absolute garbage for people working in 20th-C. US history of any kind; supply totally swamps demand, and people with only an MA do not generally land post-secondary teaching jobs anymore--it's too easy to find a PhD, even for a bad job. The MA, for aspiring professors, is a stepping stone to a stronger program if it's even earned separately. We had a 20th C. US search a few years ago, and received well over 500 applications for one entry-level tenure-track job. And yes, we hired the person with transnational and global training--but it was someone with a PhD, several years of postdocs and teaching beyond that, and a book that was nearly out. So be very sure it's what you want to do, and have a plan B in mind, whether historical (public history) or some avocation you may have.

[edit: I should also point out that if you intend to pursue academia, restricting yourself to California will hobble you immensely. There may be reasons you don't want to move elsewhere for school or work, or can't, but be aware that those will limit your options severely and probably close off most of the best programs that will actually get you a job, and most of the jobs as well.]