Blend flour and salt. Add butter and blend, until mixture resembles coarse meal.
Add 2 tablespoons ice water and blend just until dough begins to clump together, adding more ice water by teaspoonfuls if dough is dry.
Gather dough into ball; flatten into disk. Wrap in plastic and chill 1 hour.
Roll out dough between sheets of parchment paper to 1/8-inch-thick round. Chill 15 minutes.
Preheat oven to 450°F. Combine persimmon slices, 2 tablespoons sugar, and lemon peel in medium bowl; toss to blend.
Spread preserves over crust, leaving 1 1/2-inch plain border.
Arrange persimmon slices in concentric circles atop preserves, overlapping slightly. Fold crust border up over and brush with milk.
Sprinkle crust edges and persimmon with remaining 1 tablespoon of sugar.
Bake galette 20 minutes. Reduce oven temperature to 375°F and continue baking until crust is golden, about 20 minutes longer.
Let stand at least 10 minutes. Cut into wedges and serve warm or at room temperature with a scoop of French vanilla gelato.