Arrange bread slices on a baking sheet. Drizzle 2 tablespoons olive oil on top; season with salt and pepper.
Bake in the preheated oven until crisp, about 15 minutes. Remove from oven. Keep oven on.
Heat remaining 1 tablespoon olive oil in an oven-safe skillet over medium heat. Cook and stir garlic until fragrant, 3 to 4 minutes. Stir in tomatoes; season with salt and pepper. Simmer, stirring frequently, until breaking down into a sauce, about 10 minutes.
Make 6 wells in the tomatoes using a wooden spoon. Crack 1 egg into each well. Sprinkle Parmesan cheese and basil leaves on top.
Transfer skillet to the preheated oven; bake until whites are set and yolks are still runny, about 6 minutes.
Scoop 1 egg over each slice of bread using a large spoon. Spoon remaining tomatoes over the top.