At this point your bowl with 90g of brown butter should be room temperature. If it's still very hot, place it in the freezer for a few minutes until it's only slightly warm. Then, whisk in both sugars.
Add in the egg, vanilla, and carrot. Whisk until well combined.
Add in the flour, baking soda, baking powder, salt, cinnamon, ginger, and cloves. Use a rubber spatula to fold the mixture together just until a few flour streaks remain.
Add in the toasted walnuts, and fold the mixture together just until no flour streaks remain. Cover the bowl tightly with plastic wrap and place it in the fridge for 30 minutes to firm up.*
Once you're ready to bake the cookies, preheat the oven to 350℉ / 175℃.
Use a 3 tbsp. cookie scoop to scoop out heaping scoops of dough, setting them on the cookie sheet at least 2" apart to allow room for spreading.
Bake for 10-12 minutes, or until the edges of the cookies are golden brown and the tops look only a little wet.
Immediately after taking the cookies out of the oven, take a bowl that is slightly larger than the cookies and swirl it around over the cookies to make them a little more uniform and circular.
While the cookies are cooling, make the cream cheese frosting.