Prep the pan and oven: Heat oven to 350°F (175°C).
Lightly grease a 9x9-inch square pan or line it with parchment for easy removal.
Combine dry ingredients: In a large bowl, whisk flour, granulated sugar, brown sugar, baking powder, baking soda, salt, cinnamon, and nutmeg until no lumps remain.
Mix wet ingredients: In a separate bowl or measuring jug, whisk applesauce, oil, eggs, and vanilla until smooth and glossy.
Bring it together: Pour wet ingredients into dry. Stir gently with a spatula until just combined. The batter will be thick and silky.
Do not overmix.
Fold in extras (optional): Gently fold in nuts, raisins, or chocolate chips. Keep the batter light.
Pan and top: Spread the batter evenly in the prepared pan. If using, sprinkle coarse sugar on top for a light crunch.
Bake: Bake for 28–35 minutes, until the top springs back and a toothpick inserted in the center comes out with a few moist crumbs.
Cool: Let the cake cool in the pan on a rack for at least 20 minutes.
This helps it set and slice cleanly.
Finish and serve: Dust with powdered sugar if you like. Cut into squares and enjoy warm or at room temperature.