Make the crust: In a large bowl, whisk together flour, salt, and sugar. Add cold butter cubes. Use a pastry blender or your fingers to cut the butter into the flour until the mixture resembles coarse meal with pea-sized butter pieces. Drizzle 3 tablespoons ice water over mixture and stir with a fork until dough just holds together when pinched. Add remaining water if needed. Turn dough onto a piece of plastic wrap, flatten into a disk, wrap, and refrigerate for at least 30 minutes.

While dough chills, prepare filling: Peel peaches (optional; see notes), halve, remove pits, and slice into 1/4-inch thick wedges. In a large bowl, gently toss peach slices with sugar, cornstarch, cinnamon, nutmeg, lemon juice, and vanilla. Let sit for 5 minutes.

Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.

On a lightly floured surface, roll out chilled dough into a 12-inch round, about 1/8-inch thick. Transfer to prepared baking sheet. Don't worry if edges are uneven—that's the rustic charm.

Arrange peach filling in the center of the dough, leaving a 2-inch border. Fold the edges of the dough up and over the filling, pleating as you go, to create a free-form tart. The center remains exposed.

Brush the folded crust edges with beaten egg. Sprinkle coarse sugar over the crust and over the peaches.

Bake for 30-35 minutes, until the crust is deep golden brown and the peach filling is bubbly in the center. If the crust browns too quickly, tent loosely with foil after 20 minutes.

Let cool on the baking sheet for at least 15 minutes before slicing. Serve warm or at room temperature. A scoop of vanilla ice cream or a dollop of whipped cream is lovely.