How to Make It
In a large bowl, sprinkle the yeast over the warm water and let stand until foamy, about 5 minutes. Stir in the bread flour, then add 4 cups of all-purpose flour and 2 1/2 teaspoons of kosher salt. Transfer the dough to a lightly floured surface and knead briefly, adding more all-purpose flour as necessary to form a smooth, slightly sticky dough. Coat a large bowl with vegetable spray and add the dough. Lightly spray plastic wrap and cover the dough with it. Let the dough rise in a warm place until doubled in bulk, about 1 1/2 hours. Punch the dough down and divide it into 8 balls. Flatten each ball into a disk.
Arrange the disks on 2 lightly floured large baking sheets. Cover with lightly sprayed plastic wrap and let stand at room temperature until the dough has doubled in bulk, about 1 hour.
Light a grill. Pour 1/2 teaspoon of the oil onto an unrimmed baking sheet, add a dough disk and turn to coat with the oil. working on the baking sheet, stretch the dough out to a 12-inch round.
Using a damp paper towel, coat the grill with 1 teaspoon of the oil. Carefully transfer the dough to the grill and cook over a hot fire, rotating occasionally, until crusty and dark brown on the bottom, about 3 minutes. Turn the crust over and sprinkle 1 minced garlic clove on top. Spread about 1/3 cup of the Eggplant Caviar on the pizza and top with 1 tablespoon of the Parmesan and then one-eighth of the feta. Cook the pizza, rotating occasionally, until crusty on the bottom, about 3 minutes. Garnish with a few parsley leaves, cut into wedges and serve. Repeat with the remaining ingredients to make 7 more pizzas.