Preheat the oven to 425°F (218°C). Place a rack in the center and line a baking sheet with parchment paper.
Trim the cauliflower by removing the stem and cut into evenly sized florets; halve larger florets to create flat surfaces for even roasting and easier topping.
In a large mixing bowl, combine the olive oil, minced garlic, sea salt, paprika, and black pepper. Add the cauliflower florets and 1/4 cup of the grated Parmesan, then toss until evenly coated.
Arrange the florets cut-side down on the prepared baking sheet in a single layer.
Bake for about 15 minutes, until the undersides are golden brown and starting to crisp.
Flip the florets, sprinkle with the remaining 1/4 cup Parmesan and the shredded mozzarella if using, then return to the oven and roast 6–10 more minutes until edges are golden and the cauliflower is fork-tender.
Remove from the oven and transfer to a serving dish, scattering chopped parsley over the top if desired.