Combine flour, baking powder, and salt in a bowl; set aside. Beat the butter and confectioners' sugar with an electric mixer in a large bowl until smooth. Stir in the vanilla and almond extracts and orange zest.
Mix in the flour mixture until just incorporated. Fold in the cranberries; mixing just enough to evenly combine.
Divide the dough into 2 equal portions, then roll into logs about 7 inches long. Wrap each log in wax paper or plastic wrap, and chill in the refrigerator for at least 4 hours.
Preheat an oven to 350 degrees F (175 degrees C).
Remove wax paper, and cut the cookie dough into 1/2-inch slices. Arrange the slices on a baking sheet about 1 inch apart.
Bake in the preheated oven until firm but not browned, about 10 minutes.
