1. Preheat and Prepare the Pan

Preheat your oven to 350°F (175°C). Grease a 9-inch springform pan with butter or non-stick spray to prevent the cake from sticking.

2. Mix the Dry Ingredients

In a medium-sized bowl, whisk together the all-purpose flour, baking soda, salt, cinnamon, and nutmeg. Set aside.

3. Cream Butter and Sugar

In a separate large bowl, cream together the butter and sugar using a hand mixer or stand mixer. Beat until the mixture becomes light and fluffy, about 3-5 minutes. Add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract.

4. Combine Wet and Dry Ingredients

Gradually add the dry ingredients to the creamed mixture, mixing until just combined. Be careful not to overmix, as this can make the cake dense.

5. Fold in Apples and Nuts

Gently fold in the diced apples and, if desired, chopped nuts. Make sure the apples are evenly distributed throughout the batter.

6. Pour into the Pan and Bake

Pour the batter into the prepared springform pan and smooth the top with a spatula. Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.

7. Prepare the Caramel Sauce

While the cake is baking, prepare the caramel sauce. In a small saucepan over medium-low heat, combine the brown sugar, half & half, and butter. Stir continuously until the mixture becomes smooth and thick, about 5-7 minutes. Be careful not to let it boil or burn.

8. Add the Caramel Topping

After the initial baking time, remove the cake from the oven. Drizzle the caramel sauce evenly over the top of the cake. Return the cake to the oven and bake for an additional 10 to 15 minutes, or until the caramel sets and the cake is fully baked.

9. Cool and Serve

Allow the cake to cool in the pan for about 15 minutes before removing the sides of the springform pan. Serve warm or at room temperature, with a dollop of whipped cream or a scoop of vanilla ice cream if desired.