I actually ran into a similar situation to this in my course work. Though this was within the same university. There was a subject that came up to write a paper on that I wrote a really good 20 page essay on for another class. I asked the teacher if it would be ok if I used this paper again since technically I am the one who wrote it and there shouldn't be any issues about copying other people's work. She told me that I can QUOTE my previous paper, quote my previous thoughts, but she still wanted to see my original thinking.
So basically, I ended up writing something to the effect of:
In class HUM405, I wrote a paper called "Rocks rock!" in which I discussed the ideas of _____________. In this paper, I ascertained that the studies found the data to be inconclusive. "insert a quote of your thoughts from this previous paper" (cite your paper).
That way you still are creating an original piece of work while able to use your last paper to do most of the heavy work for you. You might even find that the paper you wrote a year ago has some incorrect conclusions or that you didn't do something correctly.
You would be able to even state how, in this paper I said that XXXX would be the results but actually, I found that this isn't true and here is why. Then provide the new research to show why your previous paper was actually wrong. You can still use the same references as long as you cite them because you are more than likely going to cite them again anyways. The key though, the teacher wants to see your original work.
When they check for plagiarism, each paper gets scanned into a database that is cross checked across the country. This way, any paper submitted regardless of college is verified to be original. More than likely, your paper is already in that system that you previously wrote. If you were to submit it again, there is a good chance it would come up. Even though it is your own work, the teacher will probably talk to you about it and depending on how nice the teacher is, could still mark you for plagiarism or even a 0 for the paper. So talking to them and telling them upfront what you would like to do would be your safest bet.