For the Muscadine Sorbet:
Place the mucadines in a large bowl with the sugar, mashing the muscadines as you add them, and stirring as you go along. Add the ascorbic acid to the mixture. Process the muscadines and sugar in batches in a blender. Pour the processed fruit into an ice bath to cool quickly. Rest for 1 hour. Pass the muscadine mixture through a chinois, pressing gently on the skins. Discard the skins. Taste the mixture and season with lemon juice or sugar as needed. Chill overnight and process in a batch freezer, or freeze solid and pacotize.
For the Apple Chips:
In a small saucepot over medium heat, combine the sugar and water, heating until the sugar is completely dissolved. Stir in the ascorbic acid. Cool completely. Using an electric slicer, slice the apples as thinly as possible, dropping them into the syrup as you go. Leave the apple slices to soak in the syrup for 1 hour. Meanwhile, preheat the oven to 200°F and line a baking sheet with a non-stick baking mat. Remove the apple slices from the syrup one at a time; drain and gently pat them dry on paper towels. Reserve the syrup cold. Place apple slices onto the mat and bake until dry and firm, but have not begun to color, about 15 minutes. While they are still hot, gently peel them off the mat.
For the Cava Gelée:
Lightly spray a half sheet pan with nonstick cooking spray. Line the pan with plastic wrap. Set in the freezer to get very cold. Soak the gelatin sheets in ¼ cup of the apple juice. Heat the gelatin and apple juice over very low heat and cook gently to dissolve. Working quickly, stir in the remaining ¼ cup cold apple juice and ½ cup reserved syrup.
Pour mixture into the chilled pan. As quickly as you can, open the cava, measure out 1½ cups, and pour into the pan in the freezer. Leave the pan in the freezer for no more than 15 minutes. Transfer to the refrigerator and hold until needed.
To Assemble and Serve:
Once the Cava Gelée is fully set, cut out rounds, using a cutter just a little smaller than the apple chips. Dab a small blob of Cava Gelée on a dessert plate. Gently press one Apple Chip on the jelly, using it as glue to anchor the chip to the plate. Using a small offset spatula or thin, flexible knife, remove a slice of Cava Gelée from the pan and place it on top of the Apple Chip (making sure it is flat). Place another Apple Chip on top of the Gelée slice. Top this second chip with another slice of Gelée. Repeat this process to make a stack of four Gelée layers with five Apple Chips. Use the remaining Apple Chips and Cava Gelée to create five more stacks. Serve with a quenelle of Muscadine Sorbet.