Don't preheat the oven yet because the dough needs a quick chill.
In a bowl, sift together flour, cocoa, baking powder, and salt; set aside.
Melt the 3/4 cup of chocolate and the butter (you can use a double-boiler or melt in the microwave). Whisk in both sugars. If mixture seem very hot, let it cool for a few minutes, then stir in the egg.
Stir in the dry ingredients just until combined (do not overmix).
Using a spatula or a wooden spoon, fold in chocolate chunks and cherries.
Press plastic wrap onto surface of dough and refrigerate for at least 30 minutes.
Preheat oven at 350. Line two baking sheets with parchment paper or non-stick foil.
Drop well-rounded tablespoons of dough, about 2 inches apart, onto prepared sheets. Bake just until edges are firm - 11 to 13 minutes. Cool on baking sheets 1 to 2 minutes; transfer to a wire rack to cool completely.