Spray a 6-quart slow cooker with cooking spray or line with a slow cooker liner. Set aside.
In a medium bowl, combine the peaches, brown sugar, and cinnamon. Toss to coat. Spread peaches onto bottom of slow cooker.
In another medium bowl, combine the Bisquick mix, brown sugar, white sugar, cinnamon, nutmeg, vanilla, and milk. Stir thoroughly to remove lumps. Spread mixture evenly over peaches.
Line the edges of the top of the slow cooker with paper towels so that condensation doesn't leak into the cobbler, cover and cook on low for 3-4 hours, or until center is set.