Every piece of cake is guaranteed to have some apple slices.
Preheat oven to 350 degrees. Butter three 5 3/4-by-3 1/4-inch nonstick straight-sided mini loaf pans. Peel, core, and cut apples into 1/4-inch-thick wedges; transfer to a medium bowl. Add spices and granulated sugar; toss. Arrange in a line down center of pans so that apples stand upright.
Whisk brown sugar, flour, and salt in a large bowl. Add egg and butter; whisk until just combined. Stir in walnuts. Pour batter over apples in pans. Smooth top.
Bake until tops are deep golden brown and a cake tester inserted into centers comes out clean, 35 to 40 minutes. Let cool slightly in pans on wire racks, about 25 minutes. Run a knife around edges of cakes to loosen, and turn out each onto a large plate. Using a serrated knife, cut each cake into 6 slices, and serve.