Preheat your oven to 350°F and lightly butter a 9x13 inch baking dish. Combine the sliced apples with granulated sugar, brown sugar, flour, vanilla, cinnamon, and nutmeg in a large bowl. Toss gently until apples are evenly coated with the fragrant spice mixture.
Spread the apple mixture evenly across the prepared baking dish. Use a spatula to distribute the filling and break up any clumps. The apples should cover the bottom in a single, consistent layer for even baking.
In a separate bowl, whisk together flour, sugar, baking powder, and salt for the topping. Add softened butter and mix with a fork or pastry cutter until the texture resembles coarse breadcrumbs. This apple cobbler recipe depends on this crumbly texture for the perfect topping.
Stir the milk into the dry mixture until just combined; do not overmix. The batter should be thick and slightly lumpy. Drop spoonfuls of batter across the apple filling, leaving small gaps so steam escapes during baking.
In a small cup, mix hot water with any remaining sugar, then drizzle over the topping. Bake for 40 minutes until the topping is golden brown and apples bubble at the edges. The internal temperature should reach 165°F for food safety.
Cool for 10 minutes before serving the easy apple dessert warm. This resting period allows the filling to set slightly while remaining soft and tender. The topping will firm up beautifully during this time.