Spread the tomatoes over several layers of paper towels and sprinkle with salt. Let them drain for 30 minutes—this step is essential for removing excess moisture so the crust does not get soggy.

Stir together most of the oil and the garlic in a small bowl. In a separate bowl, mix the Parmesan, ricotta, mozzarella, and the remaining oil, then season with salt and pepper to taste.

Heat the oven to 425 degrees with a rack in the middle position. Spread the ricotta mixture in an even layer across the bottom of the tart shell.

Blot the tops of the tomatoes dry with paper towels to ensure they are as dry as possible, then arrange them in overlapping concentric circles over the cheese filling. Drizzle the garlic-oil mixture over the tomatoes.

Bake the tart on a rimmed baking sheet until the cheese is bubbling and the tomatoes look slightly wilted, 20 to 25 minutes, rotating the sheet halfway through for even heat distribution.

Allow the tart to cool on the baking sheet for at least 10 minutes, which helps the filling set for cleaner slicing. Slide the tart onto a serving board and finish with fresh basil; serve warm or at room temperature when the crust is still buttery and crisp.