Ingredients

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For the Cake

¾ cup/150 grams dark brown sugar

2 large eggs

1 cup/230 grams sour cream

½ cup/115 grams vegetable or canola oil, plus more for the pan

1 teaspoon vanilla extract

1 teaspoon ground cinnamon

½ teaspoon freshly grated nutmeg

¾ teaspoon kosher salt (such as Diamond Crystal)

1 ½ teaspoons baking powder

½ teaspoon baking soda

1 ¼ cups/160 grams all-purpose flour

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For the Apples

2 large apples, peeled and thinly sliced (such as Honeycrisp, Granny Smith or Mutsu)

2 tablespoons unsalted butter

1 tablespoon dark brown sugar

1 teaspoon vanilla extract

1 teaspoon ground cinnamon

Pinch kosher salt (such as Diamond Crystal)

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For the Crumb Topping

½ cup/65 grams all-purpose flour

¼ packed cup/50 grams dark brown sugar

¼ cup/26 grams rolled oats

½ teaspoon kosher salt (such as Diamond Crystal)

¼ cup/57 grams unsalted butter, softened

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Preparation

1. Heat oven to 350 degrees and set a rack in the center. Oil an 8-by-8-inch square metal baking pan and line the pan with a strip of parchment paper that hangs over two sides.

2. Cook the apples: In a medium skillet over medium heat, combine the apples, butter, brown sugar, vanilla extract, cinnamon and a pinch of salt. Cook the apples, stirring occasionally, until the apples soften and the juices release and start to caramelize, 5 to 10 minutes. Turn off the heat and set the pan aside while you prepare the rest of the cake.

3. Make the crumb topping: In a medium bowl, combine the flour, brown sugar, oats and salt. Add the butter and pinch it together with your fingertips until the mixture is evenly moistened and pebble-size crumbs form. Set aside.

4. Make the cake: In a large bowl, whisk the brown sugar and eggs together until light and foamy. Add the sour cream, oil, vanilla, cinnamon, nutmeg and salt, and whisk to combine. Whisk in the baking powder and baking soda, then use a flexible spatula to fold in the flour.

5. Assemble the cake: Spoon the batter into the pan and smooth the top. Arrange the apple mixture over the top of the batter in an even layer. Sprinkle the crumb topping over the apples.

6. Bake the cake for 45 to 55 minutes, until puffed and golden and a tester inserted into the center comes out clean. Serve warm or at room temperature. (The cake can be stored, loosely wrapped, at room temperature for up to 3 days.)