Begin by washing the green beans thoroughly, removing both ends, and patting them completely dry to ensure crisp roasting.
In a large mixing bowl, combine the green beans with melted butter or olive oil, minced garlic, salt, pepper, and paprika (if using). Toss well to coat all the beans uniformly.
Line a baking tray with parchment paper and spread the seasoned beans out in a single layer. Roast them in a preheated oven at 400°F (200°C) for 12 to 15 minutes, or until they reach a tender yet firm texture.
Remove the tray from the oven and evenly scatter the mozzarella and Parmesan cheeses across the beans. Return the tray to the oven and bake for an additional 2 to 3 minutes, just until the cheese is melted and beginning to bubble.
Once out of the oven, finish the dish with a generous sprinkle of chopped parsley. Serve immediately while warm.