Preheat the oven to 350°F. Place the rack in the center of the oven. Sift together the flour with the baking powder and salt. Set aside.
In the large bowl of an electric mixer, beat together the butter, brown sugar, honey, and vanilla until smooth. Add the eggs and mix until well combined. Scrape down the bowl.
On low speed, add the cherries, nuts, and chocolate. Scrape down the bowl.
Stop the mixer and add one-third of the flour mixture. Turn to low speed and combine. Stop the mixer again, add the rest of the flour mixture, and combine on low speed.
Add the carrots, and mix on low speed until incorporated. The batter will be stiff.
Using a standard ice cream scoop or a heaped tablespoon, drop batter in mounds, 2 inches apart, onto a parchment-covered cookie sheet.
Bake for 12 to 14 minutes, remove from the oven, and allow the cookies to cool completely before removing them from the cookie sheet.