Preheat the oven to 350°F. Line an 8x8 baking pan with parchment. Set aside.
In the bowl of a stand mixer, cream together butter and both sugars until light and fluffy. Add the applesauce and vanilla, blend until combined. Set aside.
Sift together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, ginger and allspice. Add the dry mixture to the wet mixture in two increments until just mixed. Do not overmix.
Transfer to baking pan and bake for 40 minutes or until the center is set.
Remove and allow to cool fully before frosting.
Frosting:
In the bowl of a stand mixer, beat together the cream cheese and butter until light and fluffy, approximately 3-4 minutes.
Add the caramel, powdered sugar and salt, blending well again until no lumps remain.
Add 1-2 tablespoons of heavy cream depending on the desired consistency of the frosting.
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