Bring a large pot of salted water to a boil. Add pasta and cook according to package instructions. Before draining, reserve at least 1 cup of the pasta water.
In a saucepan, heat olive oil over medium heat. Add garlic and tomato paste and cook for 4–5 minutes, stirring often, until the tomato paste turns from bright red to a deeper reddish-brown.
Stir in heavy cream and let it simmer for 2–3 minutes until the sauce is smooth.
Add red pepper flakes, dried basil, salt, and black pepper. Mix well.
Add the grated parmesan, butter, and ½ cup of pasta water. Stir until the sauce is creamy and glossy.
If adding sausage or chicken, stir it in at this point.
Toss in the cooked pasta and mix until evenly coated.
Serve hot, topped with more parmesan, a sprinkle of parsley, and extra chili flakes if you like it spicy.