Preheat the oven to 450F and generously butter a large rimmed baking sheet - I buy half bun pans at the restaurant supply store. Combine the grated cheeses and set aside 2 generous cups for topping.
Cook the pasta in a large pot of salted water until tender but still slightly firm; it will spend more time in the oven, so you don't want it mushy.
In a large bowl, toss together the pasta, cheeses, and salt and pepper to taste. Spread the mixture evenly in the baking sheet and pour the milk over the surface. Sprinkle the reserved cheese on top, dot with another tablespoon or two of butter and bake, uncovered, for 15-20 minutes, or until golden and crisp.