Preheat oven to 275 degrees. Using 2 baking sheets, place 2 tortillas side by side on each sheet. With a pastry brush, lightly brush each tortilla with some of the olive oil. Flip the tortillas over and brush again. Bake 8-10 minutes, flipping over the tortillas and alternating the placement of the baking sheets halway through the cooking time. Also, during the first few minutes, use a knife point to pop any air bubbles that might develop. The tortillas shouldbe golden and crisp when done. (The tortillas may be prepared to this point up to 3 days in advance. Cool completely, seal in a plastic bag, and refrigerate until ready to use.).
Sprinkle the mozzarella evenly over the 4 tortillas. Place the tomatoes over the cheese.
Combine the garlic, olive oil, and basil and drizzle the mixture over the tomatoes.
Bake about 12 minutes, or until the cheese is bubbly. Alternate the placement of the baking sheets halfway during the cooking time. Remove the pizzas from the oven, then sprinkle bits of goat cheese all over their tops. Serve immediately.