Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.

Combine brown sugar, pecans, cinnamon, and nutmeg in a bowl. Set aside.

Sift flour, baking powder, baking soda, and salt into a bowl. Set aside.

Beat white sugar and butter together in a bowl with an electric mixer until light and fluffy; beat in eggs, one at a time, beating well after each addition. Stir in apple butter, bran cereal, and vanilla extract until incorporated. Add flour mixture, alternating with sour cream, mixing well after each addition.

Pour 1/2 batter into the prepared baking dish; sprinkle with 1/2 brown sugar topping. Cover with remaining 1/2 batter; sprinkle with remaining 1/2 topping.

Bake in the preheated oven until a toothpick inserted into center comes out clean, about 40 minutes.