Blanch peaches in boiling water for 30 seconds, then transfer to an ice bath. The skins will slip off easily. Slice peaches into 1/2-inch wedges.
In a large bowl, gently toss the sliced peaches with sugar, lemon juice, cinnamon, nutmeg, vanilla extract, and cornstarch.
Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish, then transfer the peach mixture into it, spreading evenly.
Whisk together flour, both sugars, baking powder, and salt in a medium bowl.
Using a pastry cutter or your fingertips, work the cold butter cubes into the dry mixture until it resembles coarse crumbs.
Stir in 1/4 cup of boiling water until just combined. The mixture will seem a bit wet.
Spoon or drop the topping mixture over the peaches, leaving some gaps for the filling to bubble through.
Bake for 40-45 minutes until the top is golden brown and the filling is bubbling around the edges.
Allow to cool for 15-20 minutes before serving.