Preheat oven to 350. Line three baking sheets with parchment. In a medium bowl, whisk together flour, cocoa, baking powder, and salt; set aside.
Place chopped chocolate and butter in a large heatproof bowl set over a pan of simmering water; stir until melted and smooth. Remove from heat; whisk in sugars, then eggs til smooth.
Whisk in dry ingredients just until combined (do not overmix). Fold in chocolate chunks and cherries; press plastic wrap onto surface of dough and refrigerate 30 to 45 minutes.
Drop mounds of dough (equal to 2 level tablespoons), about 2 inches apart, onto prepared sheets. Bake just until edges are firm (but not darkening) 11 to 13 minutes. Cool on baking sheets 1 to 2 minutes; transfer to a wire rack to cool completely.