Preheat the oven to 425℉/220℃ and line a baking pan with parchment paper.
Slice the tomatoes in ¼" thick slices then place on a paper towel. Sprinkle on a bit of salt onto the tops to draw out the moisture while you prepare the tart.
Thaw the rough puff pastry then roll it out so it becomes slightly thinner and transfer it to the prepared pan.
Use the tip of a sharp knife to score a 1" border around the pastry.
Add the ricotta, feta, garlic powder and salt to a food processor and blend it completely.
Spread the cheese mixture evenly inside the scored border, then top completely with the sliced tomatoes. It's ok for them to overlap a bit.
Whisk together the egg with ½ teaspoon water, then brush it onto the edges of the border. Use a large knife to then cut a tiny sliver off of each side (the allows it to rise best).
Bake for 20 minutes until the edges are golden brown, then cool for 5 minutes on the pan.
Top with a drizzle of olive oil, red pepper flakes, flaky sea salt, and basil leaves. Cut with a large, sharp knife to serve.
