Preheat the oven to 375° F. Drop the butter into a 9x13 inch baking dish and place the dish in the oven to melt, about 10 minutes. To make the batter. Stir together the flour, 1/2 cup brown sugar, baking powder, cinnamon, and salt. Add the milk and vanilla, mix until just combined. In a bowl, toss the peaches with 1/4 cup brown sugar and the maple syrup. Layer half of the peaches over the melted butter. Then, pour over the batter, do not stir. Layer the remaining peaches over the batter. Bake 50-55 minutes, until the center is just set and the edges begin to brown. Meanwhile, mix the butter and maple together in a pan. Boil 2 minutes, then remove from the heat.Serve the cobbler warm or at room temp with ice cream and maple butter drizzled on top.