Add the apples and cook for about 10 to 15 minutes. Toss frequently, and cook until the apples are browned and softened.

Remove from the heat and let cool.

Preheat the oven to 300°F.

Line a muffin tin with 12 muffin papers (preferably foil papers).

Place the hazelnuts in food processor fitted with a steel blade and process until they are coarse crumbs.

Drizzle in the honey through the top of the food processor until well blended into the crumbs then stop the food processor.

Distribute the hazelnut mixture evenly between the muffin papers and pat down gently.

Place the pan in the oven and cook for ten minutes. Remove from the oven.

Fill a large roasting pan with about 1 1/2 inches of water and place in the oven.

Place the cream cheese, sour cream, sweetener, cinnamon, nutmeg, vanilla extract, lemon juice, egg yolks, salt, and caramelized apples in a clean food processor bowl fitted with a steel blade.

Process until smooth.

In a copper bowl, whisk the egg whites until they form stiff peaks. Gently fold in the batter from the food processor until well blended.

Pour the batter into the muffin tins. It is easiest if you use an ice cream scoop or large spoon. The muffins papers should be as full as you can make them.

Place the pan in the heated water bath and bake for 20 minutes.

Turn off the oven and remove the water bath from the oven.

Return just the cheesecake (without the water bath) to the warm oven and allow to sit for 40 minutes in the oven as it cools.

Chill for at least four hours before serving.