Step 1

Prepare a grill for medium indirect heat. For gas grills (with 3 or more burners), turn all the burners to medium; after about 15 minutes, turn off the middle burners and turn the remaining burners down to medium-low (you want the temperature to be 375 degrees F). For charcoal grills, bank one chimney starter full of lit and ash-covered briquettes to one side of the grill (be sure to consult the grill manufacturer's guide for best results).

Step 2

Wrap a wire cooling rack in three layers of foil.

Step 3

For the filling: Combine the peaches, brown sugar, cornstarch, jam, lemon zest, almond extract and salt in a large bowl. Set aside.

Step 4

For the crust: Pulse the flour, sugar and salt in a food processor until combined. Add the butter and pulse until the mixture looks like coarse meal. Add the vodka, 1 tablespoon at a time, and pulse until the dough pulls away from the sides of the processor and forms a ball.

Step 5

Turn the dough out onto a generously floured work surface. Sprinkle a little flour on top of the dough and roll out into a 12-inch round about 1/4-inch thick (the dough will be soft and very easy to roll). Fold the dough in half and transfer to the prepared wire rack (it's okay if the dough hangs off the sides of the rack). Unfold the dough and arrange the peaches on top in a circular pattern, overlapping slightly and leaving a 2 1/2-inch border around the edges.

Step 6

Drizzle any liquid left in the bowl over the peaches. Fold the edges of the dough up and over the peaches, pinching back together any tears in the dough. Beat the egg with 1 tablespoon water in a small bowl. Brush the edges of the dough with egg and sprinkle with the turbinado sugar.

Step 7

Place the rack on the indirect (no flame) side of the grill. Close the lid and cook until the crust is golden brown and the peaches are tender, 40 to 45 minutes.

Step 8

Remove from the grill and cool the galette to room temperature, about 1 hour. Slice and serve with ice cream if using.