In a medium bowl, stir together flour, 1/2 cup white sugar, and baking powder.
Mix in milk and 1/4 cup butter until smooth.
In a medium saucepan, stir together the brown sugar, cornstarch, and water.
Mix in the peaches and blueberries. Cook and stir over medium heat until thick and bubbly.
Mix in 1 tablespoon butter and lemon juice. Continue cooking until the butter melts.
Pour into a 1 1/2 quart ungreased baking dish. Evenly spoon batter in mounds over the hot fruit. In a small bowl, mix the coarse sugar and nutmeg, and sprinkle over the batter.
Place the baking dish on a shallow baking pan in the preheated oven.
Bake cobbler for about 35 minutes, or until bubbly and a toothpick inserted into the crust comes out clean.