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In a large mixing bowl, whisk together the flour, ginger, cinnamon, cloves, baking soda, and salt. Set aside.
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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.
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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.
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Reduce the mixer speed to low and gradually add in the dry ingredients, beating just until combined.
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Cover bowl tightly with plastic wrap and transfer to the refrigerator to chill for at least one hour (or up to one day).