6 tablespoons (3/4 stick) unsalted margarine
1/3 cup dark brown sugar
2/3 cup honey
5 medium (about 2 pounds) Granny Smith apples, peeled, cored and cut into quarters
1 1/2 cups flour
1 1/2 teaspoons baking soda
1 1/2 teaspoons baking powder
1/4 teaspoon salt
1/8 teaspoon cayenne pepper
1/4 teaspoon ground cardamom
1/2 teaspoon ground cinnamon
Finely grated zest of 1 small orange (2 teaspoons)
3 large eggs
1 cup sugar
3/4 cup vegetable oil
1 tablespoon vanilla extract
3 to 4 medium carrots, peeled and grated (about 2 cups)
2/3 cup golden raisins
2/3 cup chopped pecans or walnuts (optional; see headnote)
Position an oven rack in lower third of oven; preheat to 425 F.
Melt the margarine in a 9-inch cast-iron skillet over medium-low heat, tilting it so skillet's sides are evenly coated. Remove it from heat. Sprinkle the brown sugar evenly over skillet's bottom, then pour the honey evenly over brown sugar.
Starting from outside and working your way toward pan's center, arrange the apple pieces (cored sides up) in concentric circles. (You should be able to make 2 full circles, with 3 or 4 pieces in the center.) Work pieces in where you can if there seem to be too many; they will fill gaps during baking. Transfer to oven and bake for 25 minutes or until sugar and honey are bubbling and apples can be easily pierced with a knife. Transfer to stovetop (off the heat).
Reduce oven temperature to 350 F.
Meanwhile, whisk together the flour, baking soda, baking powder, salt, cayenne pepper, cardamom, cinnamon and orange zest in a small bowl.
Whisk together the eggs, sugar, oil and vanilla extract in a large bowl for about 1 minute or until thickened, then add flour mixture, the carrots, raisins and nuts, if using; stir until just combined.
Spoon batter evenly over apples in skillet, first over outside circle of apples, then inner apples. Use an offset spatula to carefully spread batter evenly. Return skillet to oven and bake for 35 to 40 minutes, until a toothpick inserted in center comes out clean. Run a rounded thin knife around cake's edges to loosen it. Let cake sit for a few minutes, then carefully invert it onto a cake plate. Cool completely before serving. Cooled cake can be made up to 2 days in advance and covered tightly with plastic wrap.
Makes 12 servings.