Preheat the oven to 425 degrees farenheit. Pull the puff pastry from the freezer and let sit at room temperature while you prep your tomatoes, about 20 minutes.
Halve the cherry tomatoes. Thinly slice the full sized tomatoes. Pat away any excess liquid with a paper towel and let sit for about 10 minutes.
Pull the basil leaves from the stems. Line a sheet pan with parchment paper. Spread the puff pastry sheet flat on the parchment paper. Using a knife, score the edges of the pastry, about 1/2 inch on all sides.
Cover the tart with a thick layer of mascarpone. Arrange the tomatoes on the tart, evenly spaced, then top with course sea salt and freshly ground black pepper.
Bake at 425 degrees for 25 minutes until edges are brown and tomatoes are fully cooked. Add the basil during the last 5 minutes so it does not burn. Serve warm in slices.