Roll out the sheet of puff pastry. Cut 1/2-inch strips from a second sheet of puff pastry until you have enough strips to create a "crust" around the edges of the first sheet. Dab a bit of water on each strip to attach it to the main sheet. Prick a fork in several places around the puff pastry to allow it to "breathe" while baking.

Spread pesto on the surface of the tart. Brush the exterior crust with beaten egg. Bake the crust for 10 minutes at 400 degrees.

Meanwhile, slice the tomatoes in thin slices. Set them out on parchment paper over a cooling rack and sprinkle them with salt. (This will allow them to drain off excess water.)

Remove the crust from the oven and layer the tomato slices over the crust in whatever pattern you like. Return to the oven, reduce the temperature to 375 degrees, and bake for another 20-25 minutes. Remove from oven and sprinkle with kosher salt and garnish with fresh basil leaves (optional). Serve warm or at room temperature.