American, but I studied in Durham. I don't like the "this essay will discuss" form because it seems to absolve the author for responsibility of what is written. I don't have a problem with "in this essay, I claim" constructions as long as it is in relation to your thesis and not your evidence. At some level there's breaking the fourth wall, but your ideas shouldn't just exist in space. Take responsibility for them.

But you also have to judge your teacher. If using "I" is going to set them off, don't do it. It's an unfortunate truth of academia; your grade is subject to the whims of your prof.

A lot of professional historians dont "follow the rules".

And by that I mean, there isnt really one set of rules on how to write which is accepted by the entire history community. The Chicago Manual of Style is probably the most widely accepted ruleset, but even it isnt used by every historian. Rather, most professional historians will create their own style, with its own internal consistency, and which is a result of various external factors. Publishers, professors, and peers all condition a professional historian to write the way that they do. Some write extremely poorly and break a lot of the accepted norms of academic writing. But they are all beholden to themselves, and to the person (or persons) who edit and peer-review to to-be-published work.

Emulating historians who you admire and respect can help you develop your own writing, and set you on a path to developing your own unique style and voice. However, you have to also acknowledge that you are beholden to the style preferences of your professor. If they dont want a "In this essay" or "My essay will discuss", then DONT DO IT. Theyre giving you a grade, and you need to please them to pass. Its an unfortunate part of academic work, but it really holds up at all levels of the process. If you dont follow the accepted guidelines, youre going to have a bad time.

So, my advice is to just find a different way of saying what you want to say. Instead of saying "My essay will discuss X, Y, and Z" just tell me about them, in the order in which your body touches on them. Its a classic introductory technique.

"This essay" is only correct to write if you are discussing the structural characteristics of the essay. Students frequently include it just to awkwardly start the essay, which wastes time and sounds bad. Let's give an example where you are writing an essay about Henry VIII and arguing that his departure from the church was inevitable.

Bad Example: "This essay will discuss Henry VIII and why his departure from the church was inevitable."

This is bad because it gives no information to the reader and does not justify the argument.

Good Example: "This essay will examine the pressure from the House of Lords, the stance of the Pope, and the personal motivations of Henry VIII in order to demonstrate that his departure from the church was inevitable."

This is good because it explains to the reader the main topics of your essay, how you are going to structure it, and what point you are arguing.

You can also be more literal about 'structure' in a book, for example "This book investigates the impacts of the Black Plague on social structure, polite interaction, and public infrastructure in England. Chapter 1 will discuss changes in social structure," etc.

Hopefully you'll have been given a handbook in 1st year that should cover some parts of essay writing such as using gendered nouns and your above question.

Remember, your professors will always help you if you ask. Just send an email to your tutor or the module co-ordinator if you need advice on structuring an essay. Also, at my University (Leicester), the library offered courses on how to write an undergraduate essay (the sort of do's and don't's that aren't necessarily explained outright). If yours has a similar sort of course, it might be worth a visit.

As everyone has already pointed out, follow the instructions of your professor regardless of if that fits your personal style.

However, there are good reasons to avoid using the "this essay" format, some of which have already been touched on. The rubric I use for these situations, and really all writing in general, is: Is it important to make my point? In this case, is it important that you reference your essay specifically? Just cut straight to the point.

For example: Instead of "This essay will compare the domestication of rice in east Asia and the domestication of wheat in western Asia." you could write this as "Though both are domesticated grasses, the domestication of rice in eastern Asia is very different from the domestication process of wheat in western Asia."

The second sentence has the same information as the first sentence for the most part (but also contains a lot more content and specific detail). Basically, "In this essay I will discuss" doesn't actually add any information because the reader already assumes this is the purpose of the first paragraph. If it doesn't add any information there isn't any reason to include it.

The same is true of using the first person. I don't object to using the first person in academic writing (although there are certainly people who do) so long as it actually serves a purpose. Is it really important to insert yourself into the argument by using the first person? I already know you are the one writing the paper and that the ideas are yours (otherwise you would have cited them), so does "I" really add any content or information? Some case maybe, but usually not.