Preheat your oven to 400°F (200°C).
Slice the tops off the garlic heads to expose the cloves. Drizzle with olive oil, wrap tightly in foil, and roast for 30-35 minutes, or until the cloves are soft and golden. Let cool slightly, then squeeze the roasted garlic out of the skins and mash into a paste.
In a large mixing bowl, combine the softened cream cheese, sour cream, mayonnaise, mashed roasted garlic, grated raw garlic, and lemon zest. Mix until smooth and well combined.
Fold in 1 cup of shredded mozzarella cheese, ½ cup grated Parmesan cheese, and parsley. Add the Italian seasoning, red pepper flakes, salt, and black pepper. Mix well to combine.
Transfer the mixture to a 9-inch baking dish or any oven-safe dish. Spread it out evenly. Top with the remaining ½ cup shredded mozzarella cheese and ½ cup grated Parmesan cheese.
Bake in the preheated oven for 20 minutes, or until the dip is bubbly and golden on top. For extra browning, broil for 1-2 minutes at the end, keeping a close eye to prevent burning.
Remove from the oven and let the dip cool slightly. Garnish with additional parsley.
Serve warm with crusty bread, crackers, or vegetable sticks for dipping.