Preheat oven to 400F.
Cook sausage according to package directions until no longer pink, crumble into small pieces. Drain and set aside.
In a 9x13 or larger, add olive oil, diced shallot, diced garlic, and chopped broccoli. Layer on sausage, uncooked pasta noodles, red sauce, chicken stock, and milk. Sprinkle on 1 cup mozzarella and 1/4 cup parmesan cheese.
Mix until all combined very well. Pressing down on noodles until mostly covered and coated in mixture.
Cover with foil and bake for 45 minutes. Take off foil, add remaining cheese to the top, and bake an additional ten minutes. Optional, but for extra crispy, broil for an extra 5 minutes at the end.
Sprinkle with fresh basil and let cool 15 minutes before serving.