Roll out the puff pastry into a 9-by-11-inch rectangle on a floured surface, trimming any uneven edges. Prick the inside with a fork every few inches, leaving a ½-inch border. Place it on parchment paper and freeze for 15 minutes.

Preheat the oven to 400 degrees F and set a rack in the middle of the oven.

Prepare the roasted tomatoes by cutting them into ¼-inch-thick slices. Arrange in a single layer on a baking sheet lined with parchment paper. Tuck thyme and garlic cloves into the pan. Season with flaky sea salt and freshly ground pepper. Drizzle with olive oil.

Lay a sheet of parchment on top of the puff pastry and place another baking sheet on top. Bake both the puff pastry and tray with tomatoes for 20 minutes.

Remove both the puff pastry and roasted tomatoes and let cool completely.

For the filling, blend ricotta, creme fraiche, roasted garlic cloves, and chiffonaded basil leaves in a food processor until light and smooth. Refrigerate until ready to assemble the tart.

For fresh tomatoes, line a baking sheet with 2 layers of paper towels. Cut larger tomatoes into ¼-inch-thick slices and halve cherry tomatoes. Set tomatoes in a single layer, season with salt and pepper, and cover with another paper towel. Let sit for 15 minutes to draw moisture out.

To assemble, spread the ricotta mixture over the surface of the puff pastry, leaving a half-inch border. Layer roasted tomatoes over the ricotta, followed by fresh tomatoes. Sprinkle with freshly ground pepper and garnish with chiffonaded basil. Serve immediately.