Cut dough in half. Lightly dust with flour, then roll each piece into a rectangle about 3 inches by ⅛ inch thick.
On each piece, space mozzarella cubes about 1 inch apart over one side of the dough. Fold the dough over the cheese to cover, then press firmly to seal around each cube and at the edges. Cut into individual squares.
Fry at 350°F for 3–4 minutes per batch, until crisp and golden. (Alternatively, brush with neutral oil and bake at 475°F for 10–12 minutes until golden and crisp.)
Transfer fried nuggets to a wire rack, season with flaked sea salt, and let them drain briefly.
Toss in a mixing bowl with garlic butter and grated Parmigiano.
Serve hot with a side of marinara.
