Preheat the oven to 400 degrees F (200 degrees C).

Heat 1 tablespoon olive oil in a saucepan over medium heat. Add onion and 2 cloves garlic; cook and stir until onion is soft, about 5 minutes.

Place beef in a large bowl. Add onion-garlic mixture, parsley, egg, bread crumbs, and 1 large handful of fontina cheese, reserving the rest for topping. Season with salt, pepper, and cayenne. Mix by hand until just combined. Scoop meat mixture into 24 mini muffin cups; meatballs need not be perfectly round.

Bake in the preheated oven until no longer pink in the centers, about 12 minutes. Leave oven on. Let meatballs cool briefly while you make the garlic butter.

Melt butter in a saucepan over medium heat. Add remaining minced garlic once butter starts to bubble; stir, then immediately remove from heat. Stir well and set aside.

Line a rimmed baking sheet with foil; coat foil with remaining olive oil. Transfer rolls, still attached, to the baking sheet. Cut a hole in the top of each roll, about 2/3 of the way down. Brush garlic butter over the insides and outsides of the rolls.

Bake until golden brown, about 8 minutes. Pour about 1 tablespoon tomato sauce into each hole. Stuff meatballs into the holes. Top each roll with a spoonful of tomato sauce and remaining fontina cheese. Sprinkle Parmesan cheese on top.

Continue baking until cheese is melted, 12 to 15 minutes. Garnish with more parsley. Let rolls sit for 5 to 10 minutes to firm up; transfer to a serving platter.