Use either butter or cooking spray to coat bottom and sides of baking dishes. (An 8 inch square baking pan will work or 4 individual gratin dishes.)
Preheat oven to 375 degrees.
Bring 3 or 4 quarts of water to boil in a large pot. Add 1 teaspoon of salt, then add pasta. Bring back to a boil and cook the pasta one minute less than the time listed on the package cooking directions. Drain. (If boiling the noodles far ahead of making the cheese sauce, rinse pasta in cold water to stop cooking once it’s drained.)
Meanwhile, in a large saucepan, cook frozen squash over medium heat until it is completely defrosted. Stir in milk and mix well. Bring to simmer. Add salt, dried mustard, cayenne pepper, and pepper flakes and stir.
Reduce heat to lowest simmer setting. Stir in ricotta cheese until blended with liquid sauce. Add shredded cheddar in 3 parts, stirring after each addition to combine with sauce. Stir in Pecorino Romano and stir until blended into sauce.
Add drained pasta to cheese sauce and stir to coat completely. The mixture will appear to be soupy.
Scoop cheesy pasta into prepared casserole dish or gratin dishes.
Mix breadcrumbs, 2 tablespoons remaining Pecorino Romano cheese and black pepper in small bowl. Drizzle in olive oil and stir with a fork to blend.
Top pasta with breadcrumbs, distributing evenly. (It won’t cover entire surface, but will be enough to provide good texture and crunch.)
Bake for 20 minutes, or until cheese sauce is bubbling and golden around the edges.
Put broiler on and broil for 3-4 minutes, or until breadcrumbs are toasty golden brown.