4 medium ripe peaches
1-3 teaspoons sugar (see note in Step 1 below), plus more for sugaring the crust
1 Tablespoon lemon juice
1/2 teaspoon cinnamon
Pinch of coarse salt
2 teaspoons minced fresh basil (about 20 leaves), plus more for garnish if desired
1 disk pate brisee pie crust, cold
Flour for rolling out the pastry
8 Tablespoons mascarpone cheese
1. Preheat oven to 450 degrees, with the rack in the middle position.
2. Peel and core the peaches and cut them into thin wedge-shaped slices, about 1/8 inch thick. Put the slices in a medium bowl and taste one small slice to gauge sweetness. If your peaches are extremely sweet (as they likely are at the height of ripeness), add just 1 teaspoon of the sugar. If they are less sweet, you'll want to add more sugar, up to the full 3 teaspoons if needed. Add the lemon juice, cinnamon, salt and 2 teaspoons minced basil and stir to combine.
3. Line a large baking sheet with parchment. Lightly flour a work surface and cut the disk of pate brisee into four equal pieces. Put 3 of the pieces in the refrigerator to rest while you roll out the fourth.
4. Roll the pate brisee into a circle 1/8 inch thick. Trim the rolled pastry (a bench scraper makes this easy) into an even circle roughly 6 inches in diameter. (Reserve the trimmings in case they are needed to beef up the other galettes). Line a large baking sheet with parchment paper and transfer the pastry onto the parchment.
5. Use the back of a spoon to smear 2 Tablespoons of the mascarpone cheese in an even layer to cover the center of the rolled pastry, leaving a border of about 1 1/4 inches all the way around. Arrange one-fourth of the peach slices attractively on top of the cheese in such a way that they are slightly mounded in the center, and taper a bit as they reach the edge of the circle. (For a traditional French look, you can arrange them in a circular pattern like we did, or any other pattern you like.)
6. Working section by section around the circle, carefully fold the edges of the pastry over the peaches, leaving a gap of uncovered peaches in the middle. Slide the galette to one corner of the parchment to make room for the other galettes.
7. Repeat steps 4-6 with the other three galettes. When all four have been assembled, sprinkle sugar on the outer rim of pastry surrounding each galette.
8. Slide the baking sheet into the oven and bake for 20-30 minutes, until the pastry is golden brown and the filling is puffed and bubbly. The galettes will only stay puffed for a brief few minutes after they emerge from the oven, so if you want your guests to see them at their puffiest, gather everyone a few minutes before the galettes are done. (And if you miss this window, they will still be beautiful and delicious, so not to worry either way!).
9. Garnish the galettes with additional basil if desired, and serve.