1. Stir the diced apples, sweetener, lemon juice, cinnamon, butter or salt, and optional nutmeg in a saucepan over medium heat until the apples soften, about 5 minutes.
2. Whisk cornstarch and cold water in a small bowl to form a slurry.
3. Slowly pour the slurry into the saucepan. Stir constantly for about 1 minute or until apple filling is thick.
4. Remove from the heat and let cool, then refrigerate filling loosely covered with a cloth or paper towel until cold (or overnight).
5. Place around 2-3 tablespoons of filling in the middle of an uncooked egg roll wrapper. Fold up the sides tightly, and brush water along the edges to seal in the apples.
6. Brush with oil, or spray with nonfat cooking spray. Use one of the following cooking methods.
If deep frying: Heat about 3 inches of vegetable or coconut oil in a heavy bottom pan or deep fryer to 350° Fahrenheit (176° Celsius). Drop 2 rolls at a time into the hot oil and fry for 2 minutes or until crispy. Remove with tongs and let cool on a plate lined with paper towels.
If air frying: Preheat the air fryer to 350° Fahrenheit (176° Celsius). Place rolls in a single layer and cook 7 minutes. Flip and cook an additional 2 minutes or until golden.
If baking: Preheat the oven to 350° Fahrenheit (176° Celsius). Arrange the apple pie egg rolls in a single layer on a baking sheet. Bake 25 minutes or until lightly brown with caramelized filling.
Serve the apple pie egg rolls with a dusting of powdered sugar or cinnamon sugar, or topped with vanilla ice cream and caramel sauce.