Heat oven to 500°. On a lightly floured surface, roll out pizza dough into 12 4-inch rounds, ¼ inch thick, and bake 12 to 15 minutes. (You may bake rounds a day ahead if you like; cool completely and store in airtight containers.)
Combine olives, garlic, oregano, oil, tomatoes, and paste; mix well. Spread 3 tablespoons olive mixture evenly on each round and top with goat cheese. Bake 10 to 15 minutes, until tartlets are crisp, and cheese and exposed dough are slightly browned. Top each tartlet with a fresh basil leaf.