1. For the cookies, preheat the oven to 350°F. In a bowl, mix the flour, confectioners' sugar, baking powder and salt. Using your fingertips, blend in the butter until crumbly. Make a well in the center; stir in the eggs and vanilla.
2. Knead the dough on a floured board until smooth. Shape dough into 1-inch balls; place 1 inch apart on lightly greased baking sheets. Bake for 15–20 minutes, until golden but slightly soft. Transfer to racks; let cool.
3. For the frosting, mix the confectioners’ sugar, butter, vanilla and enough water to make a thin frosting. Dip tops of the cookies in frosting, sprinkle with nonpareils (colored sprinkles) and let dry.