Step 1

Place 8 tablespoons (1 stick) of the unsalted butter in the bowl of a stand mixer. (Alternatively, place in a large bowl if using an electric hand mixer.) Place 1 cup applesauce and 1/2 cup whole or 2% milk in a medium bowl and stir to combine. Place 3 large eggs on the counter. Let the butter, milk mixture, and eggs sit at least 1 hour to come to room temperature.

Step 2

Arrange a rack in the middle of the oven and heat the oven to 350ºF. Melt 1 tablespoon of the unsalted butter in the microwave or on the stovetop. Brush a 10-cup (around 9-inch) bundt cake pan with all of the melted butter, making sure to brush the tube.

Step 3

Place 2 1/2 cups all-purpose flour, 1 1/2 teaspoons baking powder, 1 1/2 teaspoons kosher salt, 1/2 teaspoon baking soda, and 1/2 teaspoon ground nutmeg in a medium bowl and whisk to combine and aerate.

Step 4

Add 3/4 cup of the granulated sugar and 1/2 cup packed light brown sugar to the bowl of butter. Beat with the paddle attachment on medium speed until light and fluffy, about 3 minutes. Add the eggs one at a time, beating well after each addition. Add 1/4 cup vegetable oil and 1 teaspoon vanilla extract and beat until incorporated, about 1 minute.

Step 5

Reduce the mixer speed to low. Beat in 1/3 of the flour mixture, then half of the milk mixture. Beat in half of the remaining flour mixture, then the remaining milk mixture. Beat in the remaining flour mixture. Increase the speed to medium and beat until just combined, about 30 seconds more. Scrape the batter into the prepared pan and smooth out the top.

Step 6

Bake until a cake tester inserted in the cake comes out clean, 55 to 65 minutes. Meanwhile, stir the remaining 3 tablespoons granulated sugar, 1/2 teaspoon ground cinnamon, and a pinch of ground nutmeg together in a small bowl. Fit a wire rack over a baking sheet.

Step 7

Place the bundt pan on the rack. Melt the remaining 1 tablespoon unsalted butter, and immediately brush the bottom of the cake with a thin coating of butter (save the remaining butter). Sprinkle with 2 teaspoons of the spiced sugar. Let cool 45 minutes.

Step 8

Flip the cake out onto the rack. Brush all over with the remaining butter (melt again if needed). Sprinkle all over with the remaining spiced sugar. To coat the sides, gently lift small sections of the cake up from the bottom and tilt towards the center while sprinkling. Sprinkle in a few rounds, as the first few rounds will be absorbed by the cake. Serve warm or at room temperature.