Preheat the oven to 425°F (220°C) and line a sheet pan with parchment paper. Cut the puff pastry into 9 even pieces, scoring a rectangle inside each piece without cutting all the way through.

In a bowl, combine the ricotta, grated Parmigiano-Reggiano, kosher salt, black pepper, minced basil, garlic powder, and dried oregano. Whisk the mixture until smooth. In a separate bowl, whisk the egg to create an egg wash and set aside.

Arrange the puff pastry pieces about 1 inch apart on the prepared baking sheet. Spoon roughly 1½ tablespoons of the cheese mixture into the interior rectangle of each puff pastry piece. Top each with the sliced mini heirloom tomatoes. Brush the tomatoes lightly with olive oil and the edges of each pastry piece with the egg wash.

Bake for 20 minutes until the pastry is puffed and golden brown, turning the baking sheet halfway through. Remove from the oven and transfer the tartlets to a wire rack to cool. Garnish with additional basil leaves, flaky sea salt, and black pepper. Serve warm or at room temperature.