My unprofessional opinion is that it's wicked hard to have dual expertise and do both areas equally well, with both areas of expertise demonstrating equivalent proficiency. We had a recent thread touching on this in the context of Barbara Tuchman writing books on both 14th century medieval history and military history of World War One. (With a really interesting aside by /u/mikedash on one academic who did pivot between markedly different historical fields, and why -- Sir Ian Kershaw.) In a formal academic context, it's difficult to maintain the duration and depth of scholarship necessary to know one field at a professor level, and even more difficult to maintain that in two fields, especially if they're not immediately linked. That doesn't mean that nobody ever does, certainly, but it's tough and I take my hat off to people who manage it.

It depends on the fields. In the case of your professor (David Blackbourn?), it's not as crazy as one might think, because these can be mutually overlapping (e.g. you can do environmental history of Nazi Germany as a solid, singular topic that touches on many aspects of both fields of work).

In fields that are defined by a thematic approach to history (e.g., environmental history, intellectual history, history of science, history of technology, gender and history, etc.), it is common that any given scholar in that field specializes in a specific time and place (e.g., "Germany under National Socialism," "Cold War America," "Interwar France").

When one gets a PhD in most American programs, one has to do reading exams in several different subfields of history. These are essentially means of establishing a strong competency and familiarity with their existing literature, by cramming several hundred books into your brain over the course of a semester (it's both more fun, and more terrible, than it sounds). These allow you to become reasonably comfortable with a few fields of work, and are a springboard to dissertation work that allows you to really dig deeper into one or two of them. (My four fields in a history of science program, offered as just an example, were history of modern physics, history of modern biology, modern US history, and science and politics/STS.)

The actual dissertation work involves becoming the expert of your topic, which if it is a discipline-spanning topic (and many are), means becoming a master of those disciplines as well. So my topic was on the history of nuclear secrecy, which involved looking not only into Cold War history, history of secrecy practices more generally, history of nuclear technology, history of World War II, and lots of other bits.

All of this is to say, you can accommodate this kind of thing in graduate work, and even later work, pretty well, if the fields you are talking about are actually informing the same thing. It is a really different thing to totally switch horses. If I were to try to do medieval history tomorrow, I would have to almost totally re-tool as a historian — some things might be useful or applicable from what I already know, but so much would be totally different. Similarly a medievalist is not going to turn around tomorrow and become a great modernist. These are entirely different field of expertise even if they are technically in the same discipline.