In a large mixing bowl, whisk together the flour, ginger, cinnamon, cloves, baking soda, and salt. Set aside.
Remove the brown butter from the refrigerator. Microwave the butter on low power, for 10 to 15 seconds, or until it’s just softened, but not melted.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl using a handheld electric mixer, beat the softened butter until completely smooth, about 1 minute. Add in both sugars and continue beating until light and fluffy, about 3 minutes. Beat in vanilla. Add in the eggs, one at a time, beating well after each addition and scraping down the sides of the bowl as needed. Add the molasses and orange zest and beat until combined.
Reduce the mixer speed to low and gradually add in the dry ingredients, beating just until combined.
Cover bowl tightly with plastic wrap and transfer to the refrigerator to chill for at least one hour (or up to one day).