Preheat the oven to 375°F (190°C). Lightly melt the stick of butter in a small saucepan over low heat until just melted, then pour it into a 9x13-inch baking dish and tilt the dish so the butter coats the bottom evenly.
In a medium bowl whisk together the flour, 3/4 cup brown sugar, baking powder, cinnamon, and salt until evenly blended.
In a separate small bowl combine the milk and vanilla. Pour the wet mixture into the dry ingredients and stir gently with a spatula or wooden spoon until just combined—avoid overmixing so the batter stays light.
In another bowl toss the peach wedges with 1/3 cup brown sugar, 2 tablespoons maple syrup, and the lemon zest. Let the fruit sit 8–10 minutes to macerate and release a little juice.
Arrange half of the macerated peaches in an even layer over the melted butter in the prepared dish. Spoon the batter over the peaches, spreading it gently so it covers the fruit (do not stir the batter into the peaches). Arrange the remaining peaches on top of the batter.
Bake the cobbler for 45–50 minutes until the topping is puffed and golden and a toothpick inserted into the center comes out with only a few moist crumbs. If you like a little extra caramelization, switch the oven to broil for 1–2 minutes at the end—watch carefully so it doesn’t burn.
While the cobbler bakes, make the maple-butter drizzle: melt 3 tablespoons butter in a small saucepan over medium heat until foamy and fragrant, then stir in 1/4 cup maple syrup and simmer gently for about 1 minute. Remove from heat.
Remove the cobbler from the oven and let it rest 8–10 minutes to set. Serve warm with vanilla ice cream and a generous drizzle of the maple-butter sauce.