Start by washing, pitting, and slicing your fresh peaches. Place them in a mixing bowl and toss with 1/4 cup of the granulated sugar, the ground cinnamon, and nutmeg to macerate.
In a separate bowl, whisk together the all-purpose flour, remaining 3/4 cup granulated sugar, baking powder, and salt. Slowly add the whole milk, melted butter, and vanilla extract, stirring just until combined. Do not overmix.
Preheat your oven to 375°F (190°C). Lightly grease a 10-inch oven-safe skillet. Pour the peach mixture evenly into the skillet.
Dollop spoonfuls of the batter over the peaches, trying to cover most of the fruit but leaving some peaches visible. The batter will spread as it bakes.
Bake in the preheated oven for 40–45 minutes, or until the topping is golden brown and cooked through, and peach juices are bubbling around the edges.
Allow the skillet to cool slightly before serving. Serve warm, optionally topped with vanilla ice cream.