To the cooked meat, add tomatoes, broth, pasta, minced garlic, basil, oregano, and remaining 1/2 tsp salt. Stir until everything is combined.
Bring to a simmer, reduce heat to medium, and cover. Cook, stirring every few minutes, until pasta is tender, about 12-15 minutes (smaller pasta will take less time). As it cooks, add more stock or water if sauce appears too dry.
When pasta is cooked, mix in spinach and half of the cheese until the spinach is wilted and cheese is combined throughout the sauce.
Top with remaining cheese, cover and let sit until cheese is melted. Or, put the pan under the broiler (if your pan oven safe) to melt and brown the cheese.