Bring 4 quarts of heavily salted water to a rolling boil and cook spaghetti until al dente.
Reserve 1/4 cup of the starchy pasta water, then drain the spaghetti and set aside.
In a large skillet over medium-high heat, brown the Italian sausage, breaking it into small crumbles with a spatula until internal temperature reaches 160°F (71°C).
Remove the cooked sausage from the skillet and set aside; drain excess fat if necessary.
Reduce heat to medium and melt the butter in the same skillet.
Add minced garlic and red pepper flakes to the butter and sauté for 60-90 seconds until aromatic but not browned.
Add baby spinach to the skillet and toss frequently until just wilted, approximately 2 minutes.
Return the cooked sausage and spaghetti to the skillet.
Pour in the reserved pasta water, Parmesan cheese, and mozzarella cheese.
Toss vigorously over low heat until the cheeses are melted and a cohesive sauce emulsifies to coat the noodles.
Adjust seasoning with salt and black pepper and serve immediately.