Preheat the oven to 450°F. Line a baking sheet with parchment paper, and set aside.
In a small bowl (or right in the measuring cup), combine the crushed tomatoes, garlic, salt and pepper. Set aside.
Take one ball of the dough and generously flour it, your hands, and the work surface. Then press it down and gently stretch it out. Supporting the disk with your knuckles toward the outer edge and lifting it about the work surface, keep stretching the dough by rotating it with your knuckles, gently pulling it wider and wider until the disk reaches 8 inches. Alternatively, stretch the dough on the work surface by massaging it into a roundish disk about 8 inches, but don’t handle it more than necessary. This dough can be on the sticky side, so be generous with your flour as needed.
Place 2 provolone cheese slice halves overlapping on one half of the dough, leaving approximately a ½-inch border along the edge. Top with 3 sliced meatballs, ¼ cup of the tomato sauce, and ½ tablespoon grated Parmigiano-Reggiano.
Fold over the naked half of the dough to enclose it like a book. Pinch and pleat the edges to seal. Use a large spatula to gently set the half-moon shaped calzone onto the parchment-lined baking sheet. Repeat with the 3 remaining balls of dough, and the remaining filling ingredients.
Brush olive oil over the top of each calzone, and cut a couple of small slits on top to vent. Bake for about 30 minutes, until bubbly and golden. You can also broil the calzones for a couple additional minutes after baking to get an extra golden crust. Remove from the oven and let cool for about 5 to 10 minutes before serving, as the filling will be very hot.