Preheat oven to 350 degrees F (175 degrees C).
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.
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