Thaw 1 sheet of puff pastry dough in refrigerator.
Remove Boursin cheese from the refrigerator to soften.
Slice tomatoes in ¼-inch thick slices.
Arrange tomato slices in a strainer, sprinkling each layer with kosher salt. You’ll need about ¾ teaspoon salt total. Let slices drain for 20 minutes in strainer. Pat tomatoes dry with paper towels.
On a lightly floured surface, roll out puff pastry dough to ⅛ inch thick (about 10 x 12 inches), and place on a parchment paper-lined sheet pan.
Use a pastry cutter or paring knife to score a ¾-inch border around the sides of the dough without cutting all the way through the dough. Use a fork to prick the puff pastry dough inside of the border.
Soften 3 ½ ounces of Boursin (about ⅔ of the package) in the microwave for 15 seconds on power level 5, if it is not soft enough to spread easily.
Spread middle section of puff pastry with a thin layer of Boursin.
Sprinkle with 1 tablespoon chopped basil.
Layer tomato slices on top, overlapping them slightly.
Chill sheet pan in freezer for 20 minutes, while preheating oven to 400° Fahrenheit.
Drizzle tomatoes with olive oil. Sprinkle with pepper (if desired).
Make an egg wash by mixing one egg yolk with a tablespoon of water and a pinch of salt. Use a small pastry brush to brush egg wash just on the exposed border of the puff pastry dough.
Bake for 10 minutes, then crumble remaining Boursin cheese around the top of the tart.
Bake an additional 20-25 minutes, until crust is flaky and golden brown. Make sure the bottom of the tart is browned before you remove it from the oven.
Serve warm or at room temperature, garnished with more chopped fresh basil.
Notes
Storage Tips: Wrap up uneaten pieces of tart in aluminum foil and store in the refrigerator. Or put into an airtight container in the fridge. To reheat, using the oven or an air fryer is best for making sure the crust becomes crisp again.Expert Tips: The biggest danger with this tomato puff pastry tart is that the puff pastry crust gets too soggy. First, remove as much liquid as you can from the tomato slices—you can press them firmly with a paper towel. Make sure not to stack your tomato slices directly on top of each other so that you have more or less a single layer with a little bit of overlap. Also, make sure to check that the bottom of the crust is browned, before you take it out of the oven. The other important thing to watch out for is the temperature of your puff pastry dough. Warm dough means the pastry is harder to work with, and it also means the warm butter will not give you the flaky layers that make this dish so special. So put your dough back in the refrigerator if it feels too soft at any point in the recipe. Try to work quickly, without rushing. And don’t skip the step of putting the tart in the freezer before baking. That will ensure that the cold butter hits the warm heat of the oven and steams into gorgeously flaky pastry.