Heat oven to 375°F. Add butter to a 9x13-inch baking dish and melt in the oven.
Combine peaches, 1/2 cup sugar, lemon juice, 3/4 tsp cinnamon, nutmeg, and cornstarch in a saucepan.
Cook over medium heat, stirring, until juices bubble and lightly thicken, 3–5 minutes. Remove from heat.
Whisk flour, 3/4 cup sugar, baking powder, and salt in a bowl.
Stir in milk and vanilla until smooth. Do not overmix the batter.
Swirl the melted butter to coat the dish. Pour the batter evenly over the butter. Do not stir.
Spoon the warm peaches and their syrup evenly over the batter. Do not mix.
Sprinkle the remaining pinch of cinnamon over the top.
Bake until the top is deep golden and set, 38–45 minutes. Rotate the pan once.
Cool 10–15 minutes to let juices settle. Serve warm with ice cream or whipped cream.