Preheat oven to 450°. On a lightly floured surface, divide dough into four equal pieces. Using a lightly floured rolling pin or your hands, roll or stretch each piece into a 6-inch round. If dough shrinks, let it rest about 5 minutes, then roll again.
Mound equal portions of fontina in center of dough rounds. Top equally with peppers, basil, prosciutto, and goat cheese.
Gently pull half of dough over filling to make a half-moon shape. Fold bottom edge of dough over top edge and pinch firmly to seal. Brush tops of calzones lightly with olive oil. Transfer to a large baking sheet.
Bake calzones on middle rack until golden brown, 20 to 25 minutes (15 to 20 minutes in a convection oven). Let cool about 5 minutes, then transfer to plates.
Note: To make in advance, prepare through step 3, then freeze on a baking sheet. When frozen, wrap each calzone with aluminum foil and keep in freezer for up to 1 month. Bake at 375° for 30 to 35 minutes, until browned and cooked through.
Note: Nutritional analysis is per serving.