In a medium bowl, whisk dry ingredients: flour, baking soda, baking powder, ground cinnamon, ground cardamom, ground cloves, ground allspice, sea salt, and freshly grated nutmeg.
Cream softened butter in a stand mixer bowl with a paddle attachment using medium speed until smooth. Add brown sugar and continue to cream until fluffy.
Add vanilla extract and ⅓ of the flour mixture to the mixer bowl and blend on low until combined. Alternate with coffee, milk, and the remaining flour mixture until you have a smooth batter.
Transfer batter into the empty mixing bowl, then clean and dry the stand mixer bowl. Whip egg whites with ⅓ cup granulated sugar using the whisk attachment on medium-high until stiff peaks form. Gently fold whipped egg whites into the cake batter.
Spray the sides and bottoms of two 8" round cake pans with cooking spray, then line with parchment paper. Add batter, then bake in a 350°F oven for 30 minutes or until golden brown and a cake tester or toothpick inserted into the center comes out clean. Remove from the oven and cool for 10 minutes while you make the frosting.
Prepare Frosting & Frost Cake
Wash and dry mixer bowl, then beat softened cream cheese and softened butter with the paddle attachment on medium speed until combined. Add orange juice and zest and mix until blended. Gradually add powdered sugar, 1 cup at a time, and mix on low speed until fluffy.
Run a knife along the edges of the cakes and flip onto a wire rack. Once cooled, frost one of the cakes, then carefully place the second cake over it. Use the remaining frosting to frost the top of the cake.
Notes
I used two 9-½ inch pans, which were a little too big for the amount of batter. For this reason, I recommend using 8" pans instead.
I doubled the frosting ingredients because I didn't mind having leftover frosting. You may want to do the same, especially if you frost the sides of the cake too. I left it rustic.