Boil the pasta. Begin cooking the sauce while it is boiling.
Cook the sausage over medium-high heat for about 5 minutes, breaking up with a wooden spoon, until cooked through.
Pour in the garlic, spinach, and tomatoes and stir. Cook, stirring often, until the spinach becomes wilted and the tomatoes break up. This will take about 3 minutes.
Remove the sauce from heat, cover, and keep warm.
Drain the pasta and return it to its hot pot, retaining a small amount of its hot water. Stir in the sausage/spinach mixture. Add in the cheese, olive oil, salt, and pepper, combining thoroughly. Serve immediately.