Heat oven to 350°F. Line two baking sheets with parchment paper.
Whisk flour, oats, baking soda, baking powder, salt, cinnamon, ginger, and nutmeg in a bowl.
Beat butter, brown sugar, and granulated sugar until light and fluffy.
Mix in applesauce and vanilla until smooth.
Fold in grated carrots until evenly distributed.
Stir in the dry mixture just until combined; do not overmix.
Add nuts, raisins, and coconut. Stir to disperse. Chill dough 15 minutes to firm up.
Scoop about 2 tbsp dough per cookie onto sheets, spacing 2 inches apart.
Bake 11–13 minutes until set at edges and lightly golden. Cool 5 minutes, then transfer to a rack.
Beat cream cheese and powdered sugar. Add milk to reach a drizzle consistency.
Drizzle glaze over cooled cookies. Let set before serving.