Prep and preheat: Heat oven to 350°F (175°C).
Line two baking sheets with parchment paper. Lightly toast nuts in the warming oven for 5–7 minutes, then cool and chop.
Dry ingredients: In a medium bowl, whisk flour, oats, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves.
Wet ingredients: In a large bowl, whisk melted butter, brown sugar, and granulated sugar until smooth and glossy. Whisk in egg and vanilla until combined.
Grate and dry carrots: Finely grate carrots. Squeeze out excess moisture with a clean towel or paper towels. Removing moisture keeps cookies from spreading too much.
Combine: Stir the dry mixture into the wet mixture until just a few streaks of flour remain. Fold in carrots, raisins, nuts, and coconut (if using) until evenly distributed. Do not overmix.
Chill briefly: Refrigerate the dough for 20–30 minutes. Chilling helps set the butter for thicker, softer cookies.
Scoop and bake: Scoop 2-tablespoon portions (about 35–40 g each) onto sheets, spacing 2 inches apart. Gently flatten the tops with damp fingers for even baking. Bake 10–12 minutes, until edges are set and centers look slightly underdone.
Cool: Let cookies rest on the sheet for 5 minutes, then transfer to a rack to cool completely.
Make the drizzle: Beat cream cheese and butter until smooth. Mix in powdered sugar, vanilla, and salt. Add milk, 1 tablespoon at a time, until the mixture is thick but pourable.
Drizzle and set: Spoon or pipe the drizzle over cooled cookies. Let set at room temperature for 20–30 minutes, or chill for a quicker set.