Preheat the oven to 400°F.
Position an oven rack in the upper third of the oven.
Line a baking sheet with parchment paper and set aside.
Arrange the sliced heirloom tomatoes in a single layer on a paper towel-lined plate or small baking sheet.
Season both sides of the tomato slices with approximately 1/2 tsp kosher salt.
Cover the tomatoes with another layer of paper towels.
Gently press the paper towels against the tomatoes to absorb excess moisture.
Set the tomatoes aside while preparing the puff pastry.
In a small bowl, whisk together the egg and water to prepare the egg wash.
Unfold the thawed puff pastry on a lightly floured work surface.
Using a rolling pin, gently roll the puff pastry into an approximately 8 x 12-inch rectangle.
Cut the puff pastry into 8 smaller rectangles, each approximately 3 x 4 inches.
Transfer the pastry rectangles to the prepared baking sheet, spacing them slightly apart.
Using a pastry brush, lightly brush the edges of each pastry rectangle with the prepared egg wash.
Sprinkle approximately 1/4 cup shredded mozzarella cheese in the center of each pastry rectangle, leaving the edges exposed.
Crumble a small amount of Boursin Garlic & Fine Herbs cheese over the mozzarella on each pastry square.
Pat the tomato slices once more with paper towels to remove any remaining moisture.
Arrange a few tomato slices over the cheese on each pastry square.
Season the assembled pastry squares lightly with ground black pepper, if desired.
Transfer the baking sheet to the preheated oven.
Bake for 18 to 22 minutes, rotating the baking sheet halfway through the baking time to promote even browning.
Bake until the pastry is puffed, flaky, and golden brown, and the cheese is melted and bubbling.
Remove the baking sheet from the oven.
Allow the pastry squares to cool slightly on the baking sheet.
Just before serving, finish each pastry square with flaky sea salt.
Garnish with thinly sliced fresh basil.
Serve warm or at room temperature.