• Butter for the pan

Apple Topping

• 2 large tart apples
• 1 ounce (¼ stick) unsalted butter
• 2 tablespoons sugar
• 1 teaspoon cinnamon

Dry Mix

• ¾ cup all-purpose flour
• ¾ cup graham flour
• ¾ cup whole-grain pastry flour
• ⅓ cup sugar
• ⅓ cup dark brown sugar
• 1 teaspoon baking powder
• ½ teaspoon baking soda
• 1 tablespoon cinnamon
• 1 teaspoon ground ginger
• 1 teaspoon kosher salt

Wet Mix

• 2 ounces (½ stick) unsalted butter, melted and cooled slightly
• 1 cup buttermilk
• ¼ cup whole plain yogurt
• ¼ cup unsweetened applesauce
• 1 egg

1. Place a rack in the middle of the oven and preheat to 350°F. Rub a 9-inch round pan with high (2½-inch) sides with butter.
2. Peel the apples, then quarter and core them. Cut each quarter into thirds, then slice into pieces as thick as your thumb. They’ll be candy-corn-shaped, and will make a nice rustic topping for the cake.
3. Melt the ounce of butter, the sugar, and the cinnamon in a 12-inch skillet over medium-high heat until bubbly. (If you don’t have a large enough skillet, sauté the apples in two batches.) Add the apples and toss to coat them with the butter mixture, and let the apples sear for 1 minute without stirring. Cook for 6 to 10 minutes, until tender and caramelized, stirring every minute or so. In order to get color on the apples, it is important that they are tossed, left to sit for a minute, then tossed again and left to sit. As the apples cook, they will become soft and caramelized around the edges and smell like an apple pie baking.
4. Remove the caramelized apples from the heat before they become dry; scrape them onto a plate along with any buttery sauce. You will add this later as a topping.
5. Sift the dry ingredients into a large bowl, pouring back into the bowl any bits of grain or other ingredients that may remain in the sifter, and set aside.
6. Whisk together the wet ingredients until thoroughly combined. Using a spatula, scrape the wet ingredients into the dry ones and gently mix together. Scrape the batter into the buttered pan, smooth the top with the spatula, and top with the caramelized apples, evenly spreading them to the edges.
7. Bake on the middle rack for 40 to 48 minutes, rotating the pan halfway through. The cake is ready when it is golden brown and springs back when lightly touched, or when a skewer inserted in the center comes out clean. The cake can be eaten warm from the pan, or cooled, wrapped tightly in plastic, and kept for up to 2 days.