Step 1

Heat the oven to 375°F with a rack in the middle position. Mist a 9-by-5-inch loaf pan with cooking spray. Line it with an 8-by-14-inch piece of kitchen parchment, allowing the excess to overhang the long sides of the pan, then mist the parchment.

Step 2

Adjust the blade of your mandoline to slice 1/16 inch thick. Slice an apple lengthwise against the mandoline until you reach the core. Rotate the apple a quarter turn and again slice lengthwise to the core. Continue in this way until only the core remains; discard the core. The apple slices will have different shapes; this is fine. Transfer to a large bowl and slice the remaining apples as you did the first, adding them to the bowl.

Step 3

In a small bowl, whisk together the flour, baking powder, salt, allspice, cardamom, cinnamon and nutmeg. In a stand mixer with the whisk attachment, beat the eggs and sugar on medium-high until pale and thick, about 4 minutes. Reduce to medium-low, then add half of the flour mixture and mix, scraping the sides of the bowl as needed, until combined, about 30 seconds. Increase to medium-high and slowly add the milk; mix until fully incorporated, about 30 seconds. Reduce to medium-low, add the remaining flour mixture and mix until just combined, about 30 seconds. With the mixer running, slowly add the melted butter, then mix until homogeneous, about 30 seconds; the batter will be thick but pourable.

Step 4

Add about one-third of the batter to the apples. Using a silicone spatula, gently fold until the apples are lightly but evenly coated. Pour about ½ cup of the remaining batter into the prepared pan and spread it in an even layer. Layer one-third of the batter-coated apples (about 2 cups) in the pan; as much as possible, arrange the slices with a straight edge against the sides of the pan to minimize the gaps between fruit and pan around the perimeter. Spread another ½ cup batter over the apple layer, then arrange half of the remaining apples on top. Repeat the layering of batter and apples, then spread the remaining batter on top. Smooth the surface, then rap the pan against the counter to remove any air bubbles.

Step 5

Bake until the cake is golden brown, well risen and a skewer inserted at the center meets no resistance, 80 to 90 minutes. Cool completely in the pan on a wire rack, at least 2 hours; the cake will settle during cooling.

Step 6

Run a thin-bladed knife between the cake and short edges of the pan. Using the parchment overhang as handles, lift the cake out of the pan and set it on a cutting board. Carefully slide the cake off the parchment, then cut it into 1-inch slices. Serve with caramel sauce and whipped cream.