1 1/8 cups all-purpose flour
1 teaspoon cinnamon
Pinch of freshly grated nutmeg
1/2 teaspoon baking soda
1/2 teaspoon salt
1/2 cup (1 stick) unsalted butter, softened
1/3 cup plus 2 tablespoons packed light brown sugar
1/3 cup plus 2 tablespoons granulated sugar
1 large egg
1/2 teaspoon vanilla
1 cup coarsely grated carrots (2 medium)
1 scant cup walnuts (3 ounces), chopped
1/2 cup raisins
Put oven racks in upper and lower thirds of oven and preheat oven to 375°F. Lightly grease a baking sheet or line with parchment paper.
Whisk together flour, cinnamon, baking soda, and salt in a bowl.
Beat together butter, sugars, egg, and vanilla in a bowl with an electric mixer at medium speed until pale and fluffy, about 2 minutes. Mix in carrots, nuts, and raisins at low speed, then add flour mixture and beat until just combined.
Drop 1 1/2 tablespoons batter per cookie 2 inches apart on baking sheets and bake, switching position of sheets halfway through baking, until cookies are lightly browned and springy to the touch, 12 to 16 minutes total. Cool cookies on sheets on racks 1 minute, then transfer cookies to racks to cool completely.
While cookies are baking, make the cream cheese frosting.
Ice the tops of the cookies with cream cheese frosting and sprinkle with chopped nuts or sandwich flat sides of cookies together with a generous tablespoon of cream cheese frosting in between.
Cream Cheese Frosting
1/2 cup butter (1 stick)
8 oz. cream cheese
3 cups powdered sugar
1 tsp. vanilla extract
With an electric mixer, mix together the butter and cream cheese , until very smooth. Scrape down the sides and bottom of the bowl. Add the vanilla extract and the powdered sugar, mix until smooth.