Place the frozen, shredded potatoes in the bottom of a 9x13-inch glass baking dish. Evenly distribute and press up along the edges, too. Brush with the melted butter. Sprinkle potatoes generously with paprika and salt.
Bake on convection for 15-20 minutes, or regular bake for 20-25 minutes. The edges should get golden and slightly crispy on the potatoes.
Whisk together the eggs, half-and-half, and Italian seasoning. Set aside.
When the potato layer is done, lower the oven temperature to 350°F. Top potatoes with about two-thirds of the shredded mozzarella, then a layer of arugula, prosciutto, and finally the tomatoes.
Top with the remaining third of cheese, then pour the egg mixture over the entire dish. Bake at 350°F on convection for 35 minutes, or regular bake for 40 minutes.