Spray the inside of the slow cooker with nonstick cooking spray.
In a bowl, combine the sliced peaches, granulated sugar, brown sugar, and cinnamon. Stir to coat the peaches evenly.
Pour the peach mixture into the slow cooker. Evenly sprinkle the yellow cake mix over the peaches. Arrange the thin butter slices on top of the cake mix, covering as much of the dry mix as you can.
Cover the slow cooker and set it to high. Cook for about 3 to 3 1/2 hours, or until the top is golden and the peaches are bubbly on the sides.
Serve the peach cobbler warm, ideally with a scoop of vanilla ice cream.