For the apples:
For the cake batter:
Caramelize the Apples: Melt the butter in a sauté pan over medium-low heat. Stir in the brown sugar and cinnamon.
Place the apples in the pan, cut side up, and cook over very low heat until the apples are tender and nearly cooked through, about 15 minutes. Set aside to cool slightly.
When the apples are cool enough to handle, slice them lengthwise into 1/4-inch-thick slices, keeping the top 1/2-inch of the apple halves intact so that the apple halves stay intact but can be fanned.
Make the Cakes: Preheat the oven to 325˚F. Line a baking sheet with parchment paper. Wrap the bottom of six 3-inch ring molds (2 inches high) with heavy-duty aluminum foil. Spray the inside of the molds with nonstick cooking spray and sprinkle with the turbinado sugar. Place the ring molds on the lined baking sheet.
Using a stand mixer ﬁtted with the paddle attachment, mix the remaining ingredients in the mixer bowl at low speed until just combined. Make sure not to overmix the batter.
Place the caramelized apple halves, core side up, in the molds, pressing the apples down to fan out the slices. Divide the batter evenly among the ring molds and bake until a knife inserted in the middle of the cakes comes out clean, about 20 minutes. Let the cakes cool to room temperature.
Run a paring knife around the edge of each cake and gently remove the cakes from the molds. Invert the cakes so the apples are facing up.