Step 1: Position a rack in the middle of the oven and preheat to 350 degrees F.
Step 2: In a medium bowl, whisk together the flour, cinnamon, baking powder, baking soda, salt and cardamom.
Step 3: In another bowl, beat the granulated sugar and eggs for 3 minutes with electric mixer.
Step 4: With the mixer running, gradually add the oil and beat.
Step 5: Add the pumpkin puree and mix on medium speed until thoroughly combined.
Step 6: Scrape down the bowl.
Step 7: Add the flour mixture and mix on low speed until just combined.
Step 8: Do not overmix, the batter should be quite thick.
Step 9: Remove the bowl from the mixer and give the batter a quick stir by hand with a rubber spatula to ensure everything is mixed.
Step 10: Set the batter aside while you prepare the topping.
Step 11: Topping:
Step 12: In a 12-inch cast-iron skillet over medium-low heat, melt the butter.
Step 13: Once melted, swirl the pan or use a brush to lightly coat the sides of the skillet with the butter.
Step 14: Stir in the brown sugar and spread in an even layer; the sugar will not dissolve into the butter.
Step 15: Place apple slices in two concentric rings around the skillet.
Step 16: Then place a cranberry on top of each apple slice and in between the slices.
Step 17: Increase the heat to medium.
Step 18: Once the butter and sugar have reached a relatively robust bubble, allow the mixture to cook for 4 minutes.
Step 19: Remove the pan from the heat and pour the batter over the apples, gently spreading into an even layer and trying not to move the apples and cranberries.
Step 20: Transfer to the oven and bake for 30 minutes, or until puffed and golden and a cake tester or toothpick inserted in the center comes out clean.
Step 21: Let the cake cool in the skillet for 15 minutes before flipping onto a serving platter.
Step 22: You want to do this while the cake is still warm so it does not stick.
Step 23: Let cool for at least 30 minutes or to room temperature before cutting into wedges and serving.
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