Preheat oven to 325°F (160°C). Line a muffin tin with paper liners.
Mix graham cracker crumbs, sugar, and melted butter. Press about 1 tablespoon into each muffin liner. Bake for 5 minutes and set aside.
In a bowl, beat cream cheese and sugar until smooth. Add sour cream, egg, and vanilla, mixing until combined.
Divide cheesecake filling evenly among crusts. Bake 18–20 minutes, or until centers are just set. Cool completely, then refrigerate for at least 2 hours.
In a skillet, melt butter and add apples, brown sugar, cinnamon, nutmeg, and lemon juice. Cook until apples are soft. Stir in cornstarch slurry and cook until thickened.
Spoon apple topping over chilled cheesecakes. Garnish with caramel or whipped cream if desired.