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Step 1
Heat the oven to 400°F. Line a rimmed baking sheet with parchment paper. Move the parchment to a work surface. Unfold 1 package puff pastry onto the parchment (if your package has 2 sheets, place them side by side, slightly overlapping, so that they fit the baking sheet). Using a rolling pin, roll it into a rectangle about the size of the baking sheet. Transfer the puff, still on the parchment, to the baking sheet.
Step 2
Brush the edges with 1 large beaten egg to form a 1-inch border. Carefully roll about 1/2-inch of each side in on itself toward the center to form the outer rim of the tart. Prick the pastry all over inside the border with the tines of a fork. Brush the rim with the egg. Bake until light golden brown and slightly puffed, 10 to 15 minutes. Meanwhile, prepare the tomatoes and filling.
Step 3
Line a baking sheet or cutting board with a double layer of paper towels. Arrange 1 pound sliced tomatoes in a single layer on the paper towels. Sprinkle all over with 1 teaspoon of the kosher salt. Let sit for 10 minutes to draw out excess moisture. Pat the tomatoes dry with paper towels to absorb the moisture beaded on top.
Step 4
Stir 1 cup ricotta cheese, 1 finely grated garlic clove, 1 teaspoon dried Italian seasoning, the remaining 1/4 teaspoon kosher salt, and 1/4 teaspoon black pepper together in a medium bowl.
Step 5
Remove the baking sheet from the oven. If the pastry has puffed up, gently press down with a spoon to deflate.
Step 6
Dollop the ricotta mixture over the puff pastry and spread into an even layer. Place the tomato slices evenly over the ricotta, overlapping them slightly as needed to fit.
Step 7
Bake until the edges are puffed and the bottom is crisp and golden-brown, 10 to 15 minutes. Garnish with fresh basil leaves and red pepper flakes if using. Serve warm or at room temperature.