1. Before you are ready to bake the calzones, preheat the oven with a pizza stone inside to 500F for 30 minutes. Cut the eggplants into 1/4-inch slices.

2. Brush them on both sides with olive oil and season with freshly ground pepper. Grill them over a moderate fire until they are tender, only a minute or two on each side. Chop the basil. Roll or stretch half the dough into a 12-inch circle and place it on a lightly floured wooden peel or a heavily floured rimless baking sheet.

3. Brush the dough lightly with olive oil to within 1 inch of the edge and sprinkle it with dried chili flakes, according to your palate and tolerance. Working as quickly as possible, for each calzone spread half the mozzarella and fontina on one half of the dough, leaving a 1-inch border.

4. Arrange half the eggplant slices over the cheese, then sprinkle it with half the chopped basil. Distribute half the goat cheese on top. Moisten the edges of the dough with water and fold the untopped dough over the filling, trapping as much air inside as possible.

5. Press the edges together to seal the envelope and crimp them with the back of a fork. Slide the calzones onto the hot stone and bake 12 to 15 minutes, or until they are golden brown. Remove from the oven and transfer to a warm platter.

6. Brush the calzones with olive oil, sprinkle with the Parmesan and decorate each with a sprig of thyme or basil. Serve immediately.