Peel and slice the 8 peaches into 1/2-inch wedges. In a large bowl, combine the peaches with 1/4 cup sugar, 1/4 cup brown sugar, 1/2 tsp cinnamon, 1/4 tsp nutmeg, freshly squeezed lemon juice, cornstarch, and vanilla extract. Toss gently until the peaches are evenly coated and the cornstarch is fully dissolved—this will thicken the juices as they release during baking. I like to let this mixture sit for a few minutes so the flavors begin to meld before baking.
Preheat your oven to 425°F. Transfer the peach mixture from Step 1 to a 9x13 inch baking dish (or similar size). Bake for 10 minutes—this head start allows the peaches to begin releasing their juices and softens them slightly, which helps the filling cook evenly under the cobbler topping.
While the peaches bake, combine 1 1/4 cups flour, 1/4 cup sugar, 1/4 cup brown sugar, 1 1/2 tsp baking powder, and 3/4 tsp salt in a medium bowl. Add 6 tbsp cold butter cut into 1/4-inch cubes and work it into the dry mixture using your fingertips or a pastry cutter until the texture resembles coarse breadcrumbs. This creates pockets of butter that produce a tender, flaky topping. Pour in the 1/3 cup boiling hot milk and stir gently until just combined—the hot milk helps activate the baking powder for extra rise and creates a softer drop-style topping rather than a thick biscuit crust.
Remove the partially baked peaches from the oven. Using a spoon or small ice cream scoop, drop large spoonfuls of the dough from Step 3 over the hot peaches, spacing them about an inch apart—they'll expand slightly as they bake and create those signature cobbler gaps where the fruit filling peeks through. In a small bowl, mix 3 tbsp sugar with 1 1/2 tsp cinnamon, then sprinkle this mixture evenly over the dough topping. I find this cinnamon-sugar coating creates a beautiful crust and adds a delicious flavor contrast to the soft dough.
Return the assembled cobbler to the 425°F oven and bake for 30 minutes, until the topping is golden brown and the fruit filling bubbles around the edges. The cobbler is done when a toothpick inserted into the dough comes out clean or with just a few moist crumbs. Let it cool for 5-10 minutes before serving—this allows the filling to set slightly so it won't be runny when scooped, while still being warm and delicious.