Preheat the oven to 350°F. Lightly spray a loaf pan with cooking spray and line with parchment paper.
Using a mandoline set to ⅛ inch, carefully slice the peeled and cored whole apples into rings. The slices should be very thin and flexible. Use a safety guard or cut-resistant glove when slicing. Then, cut the apple slices in half and set aside.
In a medium bowl, whisk together the flour, sugar, baking powder, cinnamon, cardamom, and salt.
In a large bowl, whisk the eggs until light and foamy. Add the milk, melted butter, and vanilla extract, and whisk until fully combined.
Stir the dry ingredients into the wet mixture until just incorporated.
Add the sliced apples to the batter and gently toss until all the slices are evenly coated.
Layer the apple slices into the prepared pan a handful at a time, spreading them out and pressing down lightly as you go. Pour any remaining batter over the top and smooth it out.
Place the loaf pan on a sheet pan to catch any spills. Bake for 55–65 minutes, or until golden and a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for 30 minutes, then use the parchment paper to lift it out and transfer it to a wire rack to cool completely.