Heat the oven to 350 degrees F and arrange a rack in the middle. Whisk together the flour, baking powder, and salt in a large bowl until evenly combined; set aside.
Using a stand mixer fitted with a paddle attachment beat together the butter and sugars over medium speed until light and fluffy, about 3 minutes. Add the eggs 1 at a time, beating well after each addition. Reduce the speed to low, add the flour mixture and mix until just combined. Stir in the chocolate and cherries until they are uniformly distributed.
Scoop the dough by rounded tablespoons onto a baking sheet. Bake until the cookie edges are golden brown, about 14 minutes. Leave the cookies on the baking sheets on racks for 3 minutes. Repeat this process with the remaining dough. Using a spatula, transfer the cookies to racks to cool completely before serving.