Heat butter in a saucepan over medium-high heat until it browns. Remove from heat, cool and then chill until solid.
Pre-heat oven to 350° F. Prepare cupcake pans by filling with cupcake liners.
In a large bowl, whisk together both flours, baking powder and soda, cinnamon, ginger, salt, and allspice. In a food processor, finely grind coconut and walnuts. Add the nut mixture and carrots to the flour mixture and mix until well combined.
In the bowl of a stand mixer, beat together the browned butter and brown sugar until fluffy, about 1-2 minutes. Add the egg yolks one at a time. Then beat in the yogurt, orange juice, orange zest, and vanilla extract. Add half of the flour mixture, beating on medium-low until combined, then repeat with the remaining flour mixture.
Whisk the egg whites until stiff peaks form, then fold into the cupcake batter.
Divide batter into the cupcake liners. Bake for 12-14 minutes. Test the centers by poking a toothpick into the cupcake - if it comes out clean the cupcake is done. Let cool slightly, then remove from cupcake pans and complete cooling on a wire rack.
Cream Cheese Frosting
In the bowl of a stand mixer, beat the butter, mascarpone, vanilla seeds, and cream cheese until smooth. Add the vanilla extract, bourbon, and orange zest. Then add the confectioner's sugar in small amounts until the frosting is smooth. Chill slightly before frosting.
Pipe frosting into the centers of the cooled cupcakes, then frost the tops. Sprinkle walnuts on the frosting and chill.