Preheat the oven to 400°F. Slice the top off the garlic head, drizzle with 1 teaspoon olive oil, wrap in foil, and roast for 35–40 minutes until soft. Squeeze the cloves into a bowl and mash.
Cook capellini in salted boiling water according to package directions, usually 2–4 minutes. Reserve 1/3 cup pasta water, then drain.
Heat remaining olive oil in a large skillet. Add ground beef and cook for 6–8 minutes until deeply browned. Drain excess grease.
Season with Italian seasoning, smoked paprika, salt, and black pepper. Add butter and roasted garlic, stirring for 1 minute.
Pour in beef broth and heavy cream. Simmer gently for 3 minutes, then reduce the heat to low.
Stir in cream cheese, Parmesan, and mozzarella until fully melted into a smooth Alfredo sauce.
Add the capellini and carefully fold through the creamy beef sauce without breaking the delicate strands. Add a splash of pasta water if needed.
Serve in generously filled white bowls with the capellini spread loosely rather than tightly twisted. Spoon extra Alfredo beef sauce over the pasta and finish with parsley.