Preheat your oven to 375 degrees Fahrenheit.
Pour the melted butter into a 9-by-13-inch baking dish and tilt the dish to distribute the butter across the bottom.
In a medium-sized bowl sift together 1 cup all-purpose flour, 1 cup sugar (reserve the other cup for the peaches), 1 tablespoon baking powder, and 1/4 teaspoon salt. Add in 1 cup milk and stir just until all ingredients are combined. Pour the batter over the butter. DO NOT STIR.
In a large saucepan, combine sliced peaches, 1 cup sugar, 1 teaspoon vanilla, 1 tablespoon fresh lemon juice, and 1 teaspoon ground cinnamon. Bring this mixture to a boil, stirring constantly.
Pour the peach mixture evenly over the batter. DO NOT STIR
Bake for 40-45 minutes, or until the top is golden brown, the center no longer looks wet, and the fruit is bubbling around the edges.
Cool for about 15 minutes before serving. Serve warm with vanilla ice cream or whipped cream.