Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round or bundt pan.
In a large bowl, whisk together the applesauce, granulated sugar, brown sugar, melted butter, and eggs until smooth.
Stir in the vanilla extract.
In a separate bowl, sift or whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
Gradually fold the dry ingredients into the wet mixture until just combined; avoid over-mixing.
Fold in optional chopped walnuts or raisins if using.
Pour the batter into the prepared pan and smooth the top with a spatula.
Bake 45–55 minutes, or until a toothpick inserted into the center comes out clean.
Cool the cake in the pan for 10–15 minutes, then invert onto a wire rack and cool completely.
Whisk a glaze of powdered sugar with a little milk or lemon juice and drizzle over the cooled cake before slicing.