Slice challah into 8 1/2-inch-thick slices. Set aside.
For filling: Peel and core apple; cut into thin slices and place in small saucepan. Add sugar, cinnamon and lemon juice; bring to boil, stirring constantly. When apples start to become transparent, remove from heat and set aside for about 10 minutes.
For batter: In wide medium bowl, whisk flour and milk until no clumps remain. Add sugar, vanilla and eggs; whisk until ingredient are fully incorporated. Set aside.
To finish: Mix sugar, cinnamon and cocoa powder for coating; spread on large flat plate ; set aside.
Place mascarpone in piping bag or resealable plastic bag. Snip 1 corner if using bag. Set aside.
Heat butter in large skillet over medium-low heat. Dip bread slices, one by one, in batter on both sides. Place in skillet; cook until first side is browned, flip to brown second side. Repeat with all slices, placing them on flat surface, such as a baking sheet. Pipe mascarpone cheese in a 1/2-inch-thick layer over entire surface on half the slices. Top with thin layer of reserved apple filling and 2 slices aged cheddar. Top with remaining bread slices to close sandwich. Return sandwiches to hot skillet; cook, flipping a couple times to melt the cheeses. Bread should be crispy, a good dark brown color. Remove from skillet; place directly into reserved cinnamon-sugar-coating mix on plate. Flip to coat both sides with the mixture. Halve sandwiches and serve immediately.
- 1 challah bread loaf
For Apple Filling:
- 1 large Fuji or Gala apple
- 1/2 cup sugar
- 1 teaspoon cinnamon
- 2 tablespoons lemon juice
For Churro Batter:
- 1 tablespoon all-purpose flour
- 3/4 cup milk
- 1 tablespoon sugar
- 1 teaspoon vanilla
- 4 eggs