Preheat the oven to 350°F and line a standard 12-cup muffin tin with paper liners. Combine graham cracker crumbs with 2 tablespoons sugar and 1/4 teaspoon ground cinnamon in a small bowl, then stir in the melted butter until the mixture resembles wet sand. Distribute 1 rounded tablespoon of the crust mixture into each muffin liner and press down firmly using the base of a small glass or spoon.

In a separate large mixing bowl, beat the softened cream cheese together with 1/2 cup sugar until completely smooth. Blend in the vanilla extract, then add the lightly beaten eggs and continue mixing at low speed just until incorporated. Pour the cheesecake batter evenly over the prepared crusts.

Bake for 15 to 18 minutes, or until the centers are just set without overbaking. Remove from the oven and let cool in the muffin tin on a wire rack for 30 minutes, then refrigerate until chilled. These cheesecakes develop the best texture and flavor after sitting overnight.

For the topping, heat a small skillet over medium heat and sauté the chopped apple with 1 tablespoon butter, 1 tablespoon sugar, 1/4 teaspoon ground cinnamon, and a dash of cloves, stirring occasionally for 4–5 minutes until the apples become tender. Add the caramel topping and mix to combine. Spoon the warm topping over each chilled cheesecake just before serving.