Preheat oven to 400°F.
Roll puff pastry to 11-inch square on floured surface. Fit into a 9-inch round tart pan with removable bottom; trim pastry. Prick the bottom all over with a fork. Place in freezer for 30 minutes.
Line pastry with crumpled parchment paper filled with dried beans or other pie weights. Bake for 25 minutes in preheated 400°F oven. Remove from oven; remove parchment paper and dried beans or weights. Return to oven for an additional 10 minutes to crisp up. Let cool 10 minutes.
Meanwhile, slice tomatoes 1/4-inch thick; spread the tomatoes out over several layers of paper towels. Sprinkle with salt and let drain for 30 minutes. After 30 minutes, gently blot the tops of the tomatoes dry with paper towels before using.
In a small bowl, whisk together 1 tablespoon of the olive oil and 1 clove of minced garlic; set aside.
In a separate bowl, mix together the Ricotta cheese, Mozzarella cheese, Parmesan cheese, remaining clove of minced garlic and remaining 1 tablespoon of olive oil.
Reduce oven heat to 375° F.
Spread the Ricotta mixture evenly over the bottom of the cooled tart shell. Shingle the tomatoes in overlapping circles on top of the Ricotta mixture. Drizzle the garlic and olive oil mixture evenly over the tomatoes.
Bake the tart in a preheated 375°F oven until the cheese is bubbling and the tomatoes are slightly wilted, 20 to 25 minutes.
Allow the tart cool slightly on a wire rack for 5 minutes; sprinkle with the basil. Remove the tart from the tart pan and transfer to a serving platter or cutting board. (See Tip 3)
Yield: 6 servings. (See Tip 4)