In a large bowl, whisk flour, 1 teaspoon sugar, and ½ teaspoon salt. Cut in cold butter with a pastry cutter until mixture resembles coarse crumbs with some pea-sized butter pieces.
Drizzle in ice water, 1 tablespoon at a time, mixing with a fork until dough clumps together when pressed. Form into a disk, wrap in plastic, and refrigerate for 20 minutes.
On a lightly floured surface, roll dough to ⅛-inch thickness. Cut out 12 circles using a 4-inch cutter and press into mini tart pan cups, bringing dough slightly above the rim.
Prick the bottom of each shell with a fork and refrigerate while preparing the filling.
In a medium bowl, combine sliced peaches, ⅓ cup sugar, cornstarch, lemon juice, cinnamon, vanilla, and a pinch of salt. Toss gently and let sit for 5 minutes.
Remove chilled shells from the refrigerator. Arrange 3-4 peach slices in each shell in a fan or spiral pattern, leaving a small border of pastry visible.
Spoon accumulated peach juice over each tart and dot with a small piece of butter.
Preheat oven to 400°F (200°C). Brush exposed pastry edges with egg wash and sprinkle with turbinado sugar.
Bake for 22-25 minutes, rotating pan halfway, until crust is deep golden brown and filling is bubbling at the edges.
Cool in pan for 10 minutes, then run a thin knife around each tart and gently remove to a wire rack to cool for another 10 minutes before serving.