Heat oven to 375°F.
Combine the flour, cornstarch, both kinds of sugar, baking powder and salt in a food processor and pulse once or twice. Add the butter and pulse 10 or 20 times until the butter and flour are well combined. Add the vanilla and the egg and pulse 3 or 4 times. Add about half the milk and pulse 2 or 3 times. Add the remaining milk a little at a time, pulsing once or twice after each addition, until the dough holds together in a sticky mass.
Remove the dough from the machine to a bowl. Stir in chocolate and dried cherries. Shape into a ball; cover and refrigerate for 20 minutes.
Drop rounded spoonfuls of dough (a heaping teaspoon each) onto a lightly buttered baking sheet. If you want flat cookies, press the balls down a bit with your fingers or the back of a spatula or wooden spoon. Bake at 375°F for 12 to 13 minutes, or until the cookies are done as you like them. Cool on a rack, then store, if necessary, in a covered container.