Bring a large pot of salted water to a boil and cook the penne for 9 to 10 minutes until al dente, then drain and reserve 1/2 cup pasta water.
While the pasta cooks, melt the butter in a large skillet over medium heat for 1 minute, then add the garlic and cook for 30 seconds until fragrant.
Pour in the heavy cream and bring to a gentle simmer for 2 minutes, stirring occasionally.
Stir in the Parmesan cheese and black pepper, cooking for 1 minute until the sauce is smooth and creamy.
Add the drained pasta and baby spinach to the skillet, tossing for 1 minute until the spinach wilts and the pasta is coated, adding reserved pasta water if needed to loosen the sauce.
Season with salt to taste and serve immediately while hot.