Preheat the oven to 425ºF (219ºC) and grease an 8 x 8" (20.3 x 20.3 cm) or 2 quart baking dish.
Prepare your peaches by peeling, pitting and slicing them.(*See notes for tips on easily peeling your peaches).
Add the sliced peaches to a large bowl, along with ¼ cup of granulated sugar, ¼ cup of packed brown sugar, cinnamon, nutmeg, vanilla extract, lemon juice, and cornstarch (or arrowroot starch). Stir well to combine.
Pour the peach filling into the prepared baking dish and bake in the preheated oven for 10 minutes.
Meanwhile, add the flour, ¼ cup granulated sugar, ¼ cup brown sugar, baking powder and salt to a medium sized bowl. Whisk well to combine.
Add the sourdough discard to the bowl and stir well to combine. It will still be very dry, so don't worry if you think the consistency is off.
Add the melted butter and stir well to combine. The consistency should be moist and like a thin biscuit dough.
Remove the peaches from the oven, and scoop portions of dough all over the surface. Use an offset spatula or rubber spatula to smooth the biscuit topping all over the surface. A few pockets of peach filling showing through is totally fine.
Combine 3 tablespoons of sugar with ¾ teaspoons of cinnamon and sprinkle over the surface of the sourdough biscuit topping.
Bake in the preheated oven for 30-35 minutes, or until golden and bubbly.
Remove from the oven and allow to cool for 5 minutes before scooping into bowls. Serve with vanilla ice cream.