Preheat oven to 400℉.
Line a rimmed baking sheet with parchment paper and set aside.
Break the frozen puff pastry sheet into three equal pieces.
Place two puff pastries pieces onto the baking sheet for 10 minutes to defrost. Place the other puff pastry back in the freezer.
Gently whisk the egg and water in a small bowl to make the egg wash.
Using a pastry brush, coat the 2 puff pastries with the egg wash.
Set the baking sheet aside.
In a medium-sized baking dish add the tomatoes, salt, pepper, red pepper flakes, olive oil, balsamic vinesgar, and crushed garlic clove. You don't need to mix it.
Place booth the baking sheet with the puff pastry and the baking dish with the tomato mixture into the oven for 15 minutes or until the puff pastry is golden and puffy.
Remove the baking sheet with the puff pastry for the oven and set it aside.
Leave the tomatoes in the oven and roast for an additional 10 minutes.
Remove the baking dish with the tomatoes from the oven and spoon the tomato mixture on top of the puff pastries.
Use a spoon and clean fingers to place the goat cheese over the tomatoes.
Sprinkle the julienned basil on top.
Cut into triangles and serve immediately.