Bring 8 cups water to a boil. Add salt to taste and add pasta. Stir well to keep it from sticking and cook until just shy of al dente. Reserve 1 ½ cups of pasta water, drain pasta and set aside.
While pasta cooks, make the sauce. Melt 3 tablespoons of butter oven medium heat in a skillet. Sprinkle over flour and whisk well until combined. Cook, whisking frequently until the flour cooks and slightly darkens. It will smell slightly nutty.
Slowly add in the milk, whisking constantly to avoid lumps, until all the milk has been added. Bring up a simmer, whisking frequently. Season with salt and pepper to taste.
Add cooked pasta, peas, and enough pasta water to create a creamy consistency. Note: you might not need all of the pasta water.
Sprinkle over the parmesan, stir well and serve immediately, topping with more parmesan, as desired.