Preheat oven to 350°F Coat two large cookie sheets with nonstick cooking spray or line with parchment paper; set aside. In a large bowl, combine honey, brown sugar, and butter; beat with an electric mixer on medium speed until well mixed. Beat in oil, egg, and egg white. Stir in carrots.
In a medium bowl, stir together flours, pumpkin pie spice, baking powder, baking soda, and 1/4 teaspoon salt. Add flour mixture to carrot mixture, half at a time, stirring until moistened after each addition. Stir in the 3/4 cup nuts.
Using a tablespoon measuring spoon, drop 36 mounds of dough 2 inches apart onto prepared cookie sheets. If desired, press with moistened fingers to flatten each mound slightly. Bake for 10 to 12 minutes or until lightly browned. Transfer to wire racks; cool completely.
For drizzle, in a small bowl, combine cream cheese and powdered sugar; beat with an electric mixer on medium speed until well mixed. Beat in enough of the milk to make a drizzling consistency. Drizzle over cooled cookies. If desired, sprinkle with the 1/4 cup nuts.