Heat oven and prepare puff pastry - Preheat the oven to 425°F and line a sheet pan with parchment paper. Place puff pastry on a cutting board and slice into 9 even pieces. Use a knife to slice rectangles inside of each piece, creating roughly a quarter inch perimeter.

Make ricotta mixture and egg wash - In a bowl, combine ricotta, parmigiano-reggiano, salt, pepper, basil, garlic powder, and oregano. Whisk an egg in a small bowl and set aside to use as egg wash after assembly.

Assemble tartlets - Place the puff pastry rectangles on the baking sheet 1 inch apart. Spoon and spread roughly 1½ tablespoons of the cheese mixture in the middle rectangle of each puff pastry. Top each piece with sliced tomatoes, brush the tomatoes with olive oil, and brush the edges of each puff pastry rectangle with egg wash.

Bake - Place in the oven and bake for 20 minutes until the pastry is golden, turning the baking sheet halfway through. Remove from the oven and cool on a wire rack. Top with fresh basil, flaky sea salt, and freshly ground pepper and serve.