Preheat oven to 350 degrees. Line a 9x5 inch loaf pan with foil and spray with nonstick spray OR line with parchment OR grease and flour.
In a medium bowl, whisk together flour, ginger, cinnamon, cloves, salt, and baking soda.
In a large bowl, cream together butter, sugar, and applesauce.
Mix dry ingredients into wet ingredients until just combined.
Transfer batter to prepared loaf pan. Bake for 45-55 minutes until a toothpick inserted in the center comes out clean (a few loose crumbs are fine, no wet batter). Allow to cool completely before frosting.
To prepare the frosting, cream together butter and cream cheese. Mix in vanilla and 4 tablespoons milk. Mix in powdered sugar one cup at a time until completely incorporated. Add more milk as needed until frosting is creamy and fluffy. Spread over cooled cake. Slice and serve.
Notes
This gingerbread loaf will keep in an airtight container on the counter for up to three days. After that, refrigerate for another two days. After that, you should definitely eat it!
This loaf will keep in the freezer for up to 3 months in an airtight container or Ziplock bag. Freeze it un-iced and make the icing and add it when you're ready to eat it.
A fun way to top the icing is to sprinkle a small amount of cinnamon/sugar mixture over the top of the icing while it's still wet. Or you could even use a bit of finely crushed, crystalized ginger.