Preheat the oven to 400°F (200°C), wrap the garlic bulb in foil, and roast until soft, about 30-35 minutes. Cool and squeeze out the cloves.
Bring a large pot of salted water to a boil, cook pasta until al dente, reserve 1 cup pasta water, then drain.
Heat olive oil in a medium saucepan over medium heat, add roasted garlic, and mash it into a paste. Cook for 2 minutes.
Stir in the heavy cream and heat gently for 3-4 minutes without boiling.
Add lemon juice, lemon zest, salt, and black pepper, cooking for an additional 2 minutes to develop flavors.
Slowly fold in grated Parmesan cheese, stirring until melted and fully incorporated into the sauce.
Toss cooked pasta with the sauce, adding reserved pasta water gradually to reach desired consistency.
Remove from heat and garnish with fresh parsley before serving.