Preheat oven to 375 degrees with racks in upper and lower thirds.
Whisk together flour, cocoa powder, baking soda, and salt in a small bowl.
Beat together butter and brown sugar with an electric mixer at medium-high speed until pale and fluffy, then add eggs one at a time, beating until combined well. Reduce speed to low and add flour mixture, mixing until just combined. Add chocolate chunks, pecans, and cherries and mix until just incorporated.
Drop two level TBLE of dough per cookie about two inches apart onto two ungreased large baking sheets. With dampened fingers, flatten cookies slightly.
Bake, switching position of sheets halfway through baking, until puffed and set, 12-14 minutes. Transfer cookies to a rack to cool.