Preheat the oven to 350°F (177°C). Grease a 9×5-inch loaf pan.
Whisk the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg together in a large bowl until combined. Set aside.
In a medium bowl, whisk the oil, eggs, brown sugar, applesauce, vanilla, and carrots together until combined.
Pour the wet ingredients into the dry ingredients and gently whisk until just combined. Fold in the nuts/add-in. Batter will be semi-thick.
Spread the batter into prepared loaf pan. Bake for 55 – 65 minutes. The bread is done when a toothpick inserted in the center comes out mostly clean with zero raw batter. Remove the bread from the oven.
Cool completely in the pan set on a wire rack before removing and frosting.
Optional Frosting: Using a handheld or stand mixer fitted with a paddle or whisk attachment, beat the cream cheese in a medium bowl on medium-high speed until smooth and creamy. Beat in the butter until combined.
Add the confectioners’ sugar, vanilla, cinnamon, and a pinch of salt, then beat on low speed until smooth and creamy. Taste and add more cinnamon and/or salt if desired.
Frost cooled bread, slice, and serve.
