Preheat oven to 350°F. Line a 9x5-inch loaf pan with parchment, leaving an overhang on the long sides, and lightly coat with nonstick cooking spray.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, cardamom, and ginger until no lumps remain.
In a separate bowl, stir together the eggs, applesauce, sugar, brown sugar, melted butter, sour cream, and vanilla paste until well combined.
Add the wet ingredients to the dry and stir just until no dry streaks remain. The batter will be thick and a few small lumps are okay. Do not overmix.
Transfer the batter to the prepared pan and smooth the top with a spatula.
Bake for 55-65 minutes, until the top is a deep golden brown, the edges start to pull slightly away from the pan, and a toothpick inserted in the center comes out with just a few moist crumbs but no wet batter.
Remove from oven and let the bread cool in the pan on a wire rack for 20 minutes.
Use the parchment overhang to lift the bread out of the pan and transfer to a wire rack. Let cool completely, 30-60 minutes, before slicing with a serrated knife.