For the filling:

Preheat your oven to 375°F (190°C).
In a saucepan, combine peaches, granulated sugar, brown sugar, cinnamon, nutmeg, and lemon juice. Cook over medium heat until the mixture comes to a boil.
In a small bowl, dissolve cornstarch in cold water; stir into the boiling peach mixture. Cook and stir until thickened, about 2 minutes. Remove from heat and set aside.
For the biscuit topping:

In a large bowl, whisk together flour, granulated sugar, baking powder, baking soda, and salt.
Cut in cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs.
Stir in buttermilk just until combined.
Assembly:

Pour the hot peach filling into an ungreased 9×13-inch baking dish.

Drop spoonfuls of biscuit dough over the hot filling, covering as much of the surface as possible.

Bake for 30-35 minutes, or until the topping is golden brown and the filling is bubbly.

Serve warm with a scoop of vanilla ice cream or a dollop of whipped cream.