Preheat oven to 350º and line a baking sheet with parchment. In a bowl of an electric mixer, beat butter and sugars until light and fluffy. Add eggs, one at a time, until incorporated, then add vanilla. In a separate bowl, whisk together flour, baking soda, cinnamon, nutmeg, and salt. Add dry ingredients to butter mixture until well-combined.
Stir in carrots, coconut, raisins, and oats and mix until just combined.
Scoop 1” rounds of dough onto baking sheet. Bake until golden, 13 to 15 minutes. Let cool.
Make glaze: Beat together cream cheese, powdered sugar, milk and vanilla until combined. Drizzle glaze over each cookie and let harden before serving.