Preheat oven to 375 degrees.
Place stick of butter in a 9x13-inch pan and place pan in oven to melt the butter. Watch carefully so that the butter does not burn.
While butter is melting, toss peaches with brown sugar, 1/2 cup granulated sugar, and cinnamon.
In a medium bowl, stir together flour, remaining granulated sugar, milk, vanilla, and salt.
Once butter has melted, remove pan from oven and pour batter into pan.
Spoon peaches evenly on top of batter.
Place pan in oven and bake for 40 to 45 minutes.
Serve warm with vanilla ice cream.