Preheat the oven to 350 degrees F and grease a 9-inch springform pan.
In a medium mixing bowl, whisk together the all-purpose and rye flours, baking powder, cinnamon, cardamom, and salt.
In a large mixing bowl, cream the butter and sugar until pale and silky, about 3 minutes, scraping down the sides of the bowl as needed. Stir in the honey and vanilla extract. Add the eggs, one at a time, mixing well between additions.
Tip the flour into the batter and stir until incorporated.
Spread half the batter into the prepared pan. Arrange half the apple slices over this, then spread the remaining batter on top. Arrange the remaining apple slices in a decorative circular pattern, starting in the center and working your way out. Dust cinnamon over the top.
Bake for approximately 1 hour, until a toothpick inserted in the center comes out clean. Cool on a baking rack, then remove from pan.
