Preheat oven to 350F (175C).
In a large mixing bowl, combine butter and sugars and use an electric mixer (or a stand mixer fitted with the paddle attachment) and beat until creamy, light, and fluffy (about 1-2 minutes).
Add eggs and vanilla extract and stir well. Pause occasionally to scrape down the sides and bottom of the bowl.
In a separate, medium-sized mixing bowl, combine flour, baking soda, nutmeg, and salt.
Gradually add dry ingredients to the wet, pausing periodically to scrape down the sides of the bowl with a spatula.
Stir in oats until completely combined.
Add carrots and walnuts/pecans (and raisins, if using).
Drop cookies by 2-Tablespoon-sized scoops (43g) onto parchment paper-lined cookie sheet, spacing cookies at least 2" (5cm) apart. For more uniform cookies, roll the dough into a smooth ball between your palms (dough is sticky!). Bake 11-12 minutes on 350F (177C). Cookies may appear slightly underbaked at their centers still.
Allow cookies to cool completely on baking tray before decorating with icing.
For Frosting
Combine butter and cream cheese in a large mixing bowl (or bowl of stand mixer fitted with paddle attachment) and beat until smooth and creamy,.
Gradually add powdered sugar, about half a cup at a time, scraping down the sides of the bowl as needed.
Stir in vanilla extract.
Add corn starch and stir.
Spread frosting onto cookies or transfer frosting into a piping bag fitted with a Ateco 846 tip and pipe on top of cooled cookies.