Preheat the oven to 375 degrees.
MAKE THE BECHAMEL. In a medium-sized saucepan, melt the butter.
Add the flour and whisk to create a paste.
While whisking constantly, slowly add the milk.
Bring to a boil and cook, whisking constantly, for 2 minutes.
Season with salt, to taste.
Spread 1 cup of the Bolognese onto the bottom of a 9”x13” casserole dish.
Place a single layer of noodles over the sauce, breaking them as necessary to fit the casserole dish.
Spread 1 ½ cups of Bolognese evenly over the noodles.
Spread ⅔ cup of the bechamel evenly over the Bolognese, and sprinkle with a quarter of the pecorino.
Repeat the layers 3 more times, using up the remaining ingredients.
Cook, uncovered, for 45 minutes. Let sit for 10 minutes before serving.