Heat olive oil in a large deep skillet or Dutch oven over medium heat.
Add the Italian turkey sausage, breaking it up with a spoon, and cook until browned and cooked through, about 5-7 minutes.
Add the chopped onion and cook until softened, about 3 minutes.
Stir in the minced garlic, dried Italian seasoning, crushed red pepper flakes, salt, and black pepper. Cook for 1 minute until fragrant.
Add the uncooked penne pasta, chicken broth, and diced tomatoes with their juice. Stir to combine.
Bring the mixture to a boil, then reduce heat to medium-low. Cover and simmer for 12-15 minutes, stirring occasionally, until the pasta is tender and most of the liquid is absorbed.
Stir in the heavy cream and fresh baby spinach. Cook for 2-3 minutes until the spinach wilts and the sauce becomes creamy.
Remove from heat and stir in the grated Parmesan cheese until melted and well combined.
Serve immediately, garnished with additional Parmesan if desired.