For the cookies: Preheat the oven to 350
Line 3 baking sheets with parchment paper; set aside.
Beat the butter, brown sugar, and granulated sugar in the bowl of a stand mixer
fitted with the paddle attachment on medium speed until pale and creamy, about
3 minutes. Add the eggs and vanilla extract. Beat until well combined, stopping
to scrape the sides of the bowl, as needed.
Whisk together the flour, cinnamon, ground ginger, baking powder, baking soda,
and salt in a medium bowl. Gradually add the flour mixture to the butter mixture
with the mixer on low. Beat until well combined, about 1 minute. Stir in the
carrots and walnuts.
Drop spoonfuls (about 2 tablespoons each) of the dough on the prepared baking
sheets using a 1 3/4-inch cookie scoop, spacing at least 2-inches apart. Bake two
pans at a time, rotating halfway through cooking, until the cookies are lightly
browned on the edges, 12 to 14 minutes. Cool the cookies on the pans for 3
minutes. Transfer to a wire rack to cool completely, about 30 minutes. Repeat
with the remaining cookies.
For the frosting: Beat the cream cheese and butter in the bowl of a stand mixer
fitted with a paddle attachment on medium speed until smooth, about 3 minutes.
Add the powdered sugar and vanilla with the mixer on low, beating until
combined. Increase the speed to medium and beat until fluffy, about 2 minutes.
Dollop a spoonful of frosting on the top of each cookie and spread all over the
top. Sprinkle with orange jimmy sprinkles or chopped toasted walnuts.