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 create a quarter-inch border inside each piece (don't cut all the way through!).
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.
Toss the cut tomatoes in olive oil and a pinch of salt.
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 of each puff pastry. Top each piece with the tomatoes and brush the edges of each puff pastry rectangle with egg wash.
Place in the oven and bake for 20 minutes until the pastry is golden, turn after 10 minutes. Remove from the oven and cool on a wire rack. Top with fresh basil, flaky sea salt, freshly ground pepper, and/or hot honey to serve.
Substitutions:
Artichokes and olives - add sliced marinated artichokes and olives for extra flavor and texture.
Goat cheese - substitute for parmigiano-reggiano
Mozzarella - substitute for parmigiano-reggiano
Cream cheese or mascarpone - substitute for ricotta
Garlic - use chopped garlic instead of garlic powder for a more pungent aroma.
Thyme & Rosemary - substitute for oregano
Variations:
Spicy - add red chili pepper flakes to ricotta mixture
Prosciutto - add crispy prosciutto to the topping for a savory addition.
Pesto - Add pesto to the ricotta mixture
Lemon - squeeze a little lemon juice or lemon zest into ricotta mixture or on top
