Preheat the oven to 350°F or 175°C and grease a 9-inch square baking pan. Line the bottom with parchment when you plan to remove the whole cake.
Whisk flour, baking soda, cinnamon, ginger, nutmeg, and salt in a medium bowl. This distributes the spices evenly throughout the cake.
In a larger bowl, whisk oil, brown sugar, eggs, vanilla, and applesauce until smooth. The mixture may look slightly loose, which is expected.
Fold the dry ingredients into the wet mixture using a spatula. Add the diced apple and stir only until the batter is evenly combined.
Pour the batter into the pan and smooth the top. Bake for 32 to 37 minutes, until the center springs back when lightly touched.
Cool the cake completely before dusting with powdered sugar. Slice directly in the pan or lift it out using the parchment before cutting.
