Remove the dough from the refrigerator to bring to room temperature. Preheat the oven to 475°F. Wash and dry the fresh produce. Halve the tomatoes. In a bowl, combine the mozzarella (tearing into bite-sized pieces before adding), ricotta, parmesan, fontina, and a drizzle of olive oil; season with salt and pepper. Stir to combine.

Lightly oil 1 sheet pan (or 2 sheet pans for 4 servings). Divide the dough into 2 equal-sized portions (or 4 portions for 4 servings). Using your hands, gently stretch the dough into ¼-inch-thick rounds (if the dough is resistant, let rest 5 minutes). Carefully transfer to the oiled sheet pan(s). Evenly divide the filling among one half of each round, leaving a 2-inch border between the filling and the edges of the dough. Fold each round in half over the filling. Using a fork, crimp the edges of the dough to seal. Cut 4 evenly spaced slits on an angle across the top. Drizzle or brush the tops with olive oil.

Bake the calzones, rotating the sheet pan(s) halfway through, 14 to 18 minutes, or until golden brown (some filling may ooze out). Remove from the oven and let stand at least 2 minutes. Carefully transfer to a cutting board. When cool enough to handle, cut into equal-sized pieces. Drizzle or brush the tops with olive oil.

Meanwhile, in a medium nonstick pan (or large for 4 servings), heat a drizzle of olive oil on medium-high until hot. Add the halved tomatoes. Cook, stirring occasionally and pressing down gently with the back of a spoon, 3 to 4 minutes, or until softened. Add the tomato sauce (carefully, as the liquid may splatter), butter, capers, and as much of the chile paste as you'd like, depending on how spicy you'd like the dish to be. Cook, stirring frequently, 1 to 2 minutes, or until combined and heated through. Turn off the heat. Taste, then season with salt and pepper if desired. Serve the baked calzones with the sauce on the side. Enjoy!