Preheat oven to 375°F (190°C). Peel (optional), pit and slice enough ripe peaches to measure 4 cups (about 4 medium peaches). Slice into 1/2-inch wedges.

Mix filling

In a large bowl combine 1 cup granulated sugar, 1/4 cup light brown sugar, 2 tablespoons cornstarch, 1 tablespoon lemon juice, 1 teaspoon vanilla, 1/2 teaspoon ground cinnamon and 1/8 teaspoon kosher salt. Toss the peach slices in the mixture until evenly coated and let sit 10 minutes so the fruit releases juices and the cornstarch begins to absorb.

Assemble filling in dish

Transfer the peach mixture, including accumulated liquid, into a 9x9-inch or 8x10-inch baking dish, spreading into an even layer. Gently press fruit down so juices distribute. Set aside while you prepare the topping.

Biscuit Topping

Combine dry ingredients

In a medium bowl whisk together 2 cups all-purpose flour, 1/4 cup granulated sugar, 2 teaspoons baking powder and 1/2 teaspoon kosher salt until evenly combined.

Cut in butter

Cut 1/2 cup (1 stick) cold unsalted butter into 1/2-inch pieces and use a pastry cutter, two forks or your fingertips to work the butter into the flour mixture until the texture resembles coarse meal with some pea-sized pieces of butter remaining.

Mix wet ingredients

In a small bowl whisk together 3/4 cup milk, 1 large egg and 1/2 teaspoon vanilla until smooth.

Form biscuit dough

Pour the wet mixture into the flour-and-butter mixture and gently fold with a spatula just until a shaggy, slightly sticky dough forms. Do not overmix; small pockets of flour are fine.

Portion topping

Using a spoon or small ice cream scoop, drop rounded tablespoons or 10–12 mounds of dough over the peach filling, spacing them so gaps remain for steam to escape. The dough will expand and create a cobbled appearance.

Finishing and Baking

Brush and sugar

Brush the biscuit tops lightly with 2 tablespoons melted butter and sprinkle with 1 tablespoon turbinado or coarse sugar for a crunchy, caramelized finish.

Bake

Place the baking dish on a rimmed baking sheet to catch any overflow and bake in the preheated 375°F (190°C) oven for 35–45 minutes, until the topping is golden brown and the peach filling is bubbly and thickened (center will bubble). If the topping browns too quickly, tent loosely with foil for the last 10 minutes.

Rest

Remove from oven and let the cobbler rest 10–15 minutes to allow the filling to set slightly. This makes serving neater and allows juices to thicken further.

Serve

Spoon warm cobbler into bowls and serve with optional heavy cream or vanilla ice cream if desired.