Combine flour, baking powder, and salt in a bowl.

Beat butter with an electric mixer until creamy. Gradually add sweetener and mix well. Add eggs one at a time, blending well after each addition, then stir in vanilla. Gradually beat in flour mixture until just blended.

Divide the dough in half, shape into circles, wrap tightly with plastic wrap, and chill for about 1 hour until slightly firm.

Preheat the oven to 325°F (165°C).

Remove dough from refrigerator, roll to 1/8-inch thickness on a floured surface, cut into shapes with cookie cutters, and transfer to cookie sheets. Sprinkle with colored sugar.