Preheat oven to 400 degrees F.
Make Pesto: Combine basil, garlic, Parmesan, Pecorino, and pine nuts in food processor or blender. Slowly drizzle in extra virgin olive oil until fully incorporated. Season with kosher salt and cracked black pepper. Arrange bread on rimmed baking sheet. Brush with olive oil and rub with cut side of garlic. Bake until beginning to crisp, about 8 minutes.
While bread crisps, make pesto and halve cherry tomatoes lengthwise. Top crostini with pesto spread, fresh mozzarella and grape tomato slice.