In a medium mixing bowl, whisk together the flour, cinnamon, ginger, cardamom, cloves and nutmeg, baking soda and salt until well combined.
1¾ c (210 g) all purpose flour, 1 teaspoon ground cinnamon, 1 teaspoon ground ginger, ½ teaspoon ground cardamom, ½ teaspoon ground cloves, ½ teaspoon ground nutmeg, ¾ teaspoon baking soda, ½ teaspoon salt
Cream the brown butter and light brown and granulated sugars together on medium speed until well combined, about 1-2 minutes. On low-medium speed, beat in the egg, yolk and vanilla extract about 20 seconds before adding the next. Gently fold in the shredded carrots. 1 cup (226 g) brown butter, ¾ cup (150g) light brown sugar, ¾ cup (150g) granulated sugar, 1 large egg (US), room temperature, 1 large egg yolk (US), room temperature, 2 teaspoon (10ml) vanilla extract, 1 cup (110g) finely shredded carrots
On the lowest speed setting or by hand, mix the dry ingredients to the wet until just combined. Stir in the oats until just combined. Cover the carrot cake cookie dough to chill in the fridge for 2 hours. 2½ cups (215g) old fashioned or rolled oats
Preheat the oven to 375 F (190 C) for about 20-30 minutes before baking the cookies. Line a large baking sheet with parchment paper. Pull the cookies out to room temperature 10 minutes before you’re ready to bake. Using a medium cookie scoop, scoop about 2 tablespoons (30 g) cookie dough, roll them into balls and place them about 3-inches (8 cm) apart on the baking sheet. The cookies will spread while baking.
Bake the cookies for 10-14 minutes or until the edges of the cookies are set and golden brown. The centers will look puffed up. Cool the cookies on the hot baking sheet for 5-10 minutes before transferring them to a cooling rack to fully set. Cream together cooled and softened brown butter with the room temperature cream cheese until creamy and well combined, about 4-5 minutes on low speed. Stop and scrape down sides of bowl as needed.
½ cup (113 g) browned butter, 4 oz. (113g) cream cheese, softened to room temperature
Mix in the sifted powdered sugar ½ cup (60 g) at a time, beating each addition of powdered sugar until incorporated. Scrape down sides of mixing bowl as needed. Once all the sugar has been added, mix in the vanilla extract, 1 tablespoon (15 ml) milk and salt. Beat on high until the buttercream is fully incorporated and desired consistency. If the buttercream is too thick, add an additional 1-2 tablespoon (15-30 ml) milk of choice, beating until well incorporated. 1 teaspoon (5ml) vanilla extract, 2½ - 3 cups (300 - 360g) powdered sugar, sifted, 1-3 tablespoon (15-45ml) milk, as needed
Using a small offset icing knife, spoon or piping bag with piping tip of choice, apply the desired amount of frosting to the top of each carrot cake cookie. Sprinkle chopped nuts on top if you like.