Adjust oven rack to center and heat to 325°F. Grease 2 loaf pans with unsalted butter and line with parchment paper, ensuring some paper overhangs edges.
In a medium saucepan over low heat, combine butters, brown sugar, molasses, honey, and coffee. Stir frequently until butter is melted but not browned and all ingredients are well combined. Remove from heat and transfer mixture to a large bowl. Set aside to cool.
Meanwhile, in a medium mixing bowl, combine flours, cinnamon, ground ginger, baking soda, salt, allspice, and cloves. Set aside.
When butter mixture is just warm to the touch, add eggs, one at a time, incorporating each fully. Stir in milk. Carefully fold dry ingredients into wet ingredients, mixing gently but thoroughly; there should be some lumps in the batter. Add fresh ginger, and stir to combine.
Divide batter evenly between the two prepared pans. Bake 55 minutes or until tops of the cakes spring back when pressed.
Remove cakes from oven, set pans on a wire rack, and let cool 10 minutes. Next, slowly lift cakes from pans using edges of parchment paper. Set on wire rack to cool completely. While cakes are cooling, prepare whipped crème fraîche.