Coat the inside of a 5- or 6-quart slow cooker with nonstick cooking spray. Make sure the bottom and lower sides are covered because the sweet apple juices can become sticky.
Place the apples in a large bowl and add brown sugar, granulated sugar, cinnamon, lemon juice, vanilla, and cornstarch. Toss until the slices are evenly seasoned.
Spoon the apple mixture into the slow cooker and spread it into a level layer. Any seasoning left in the bowl can be scraped over the fruit.
Cut each biscuit into two or four pieces, depending on its size. Arrange the pieces over the apples with a little space between them, then brush the tops with melted butter.
Lay a clean kitchen towel across the top of the cooker before adding the lid. Cook on high for 2 to 2 1/2 hours or on low for about 3 hours, until the biscuits are cooked through.
Remove the lid carefully so condensation does not drip onto the cobbler. Let the dessert stand for 10 minutes, then serve warm with whipped cream or vanilla ice cream.
