Melt butter in bottom of a 1 1/2 to 2- quart casserole or souffle dish which will fit in the crockpot. Sprinkle with 2 tablespoons brown sugar and 1/2 teaspoon cinnamon. Add apples. Whisk eggs, milk, and apple juice together; mix in remainder of brown sugar, 1 teaspoon cinnamon, and the bread pieces.
Place a trivet or aluminum foil ring in the crockpot. Pour 3/4 cup hot water into the the crockpot. Place the casserole dish on the ring in the crockpot.
Cover and cook on high for 2 1/2 hours, until knife inserted comes out clean.
Serve warm with vanilla ice cream.