Preheat the Oven: Preheat your oven to 350°F (175°C). Grease a 9-inch springform pan thoroughly.
Prepare the Dry Ingredients: In a small bowl, sift together the flour, baking soda, salt, cinnamon, and nutmeg.
Cream Butter and Sugar: In a large mixing bowl, beat the butter and sugar together until smooth and fluffy. Add the eggs one at a time, mixing well after each addition, then add the vanilla.
Combine Ingredients: Gradually mix the dry ingredients into the wet mixture until just combined. Gently fold in the diced apples and nuts if using.
Bake the Cake: Pour the batter into the prepared pan and bake for 35-40 minutes.
Make the Caramel: When the cake has been baking for about 30 minutes, begin the caramel sauce. In a small saucepan over medium-low heat, combine the brown sugar, half-and-half, and butter. Stir frequently until the mixture is smooth and well combined; there's no need to bring it to a full boil.
Add the Caramel to the Cake: Remove the cake from the oven and pour the caramel sauce evenly over the top. Return the cake to the oven and bake for an additional 10-15 minutes or until the caramel is bubbling and the cake is fully cooked through in the center.
Cool and Serve: Let the cake cool in the pan for at least 15 minutes before slicing. Serve warm or at room temperature.