BEAT butter, granulated sugar and vanilla in mixer bowl on medium speed until light and fluffy, about 3 minutes. ADD egg and egg yolks; BEAT on low speed until blended. Gradually ADD flour and salt, beating just until blended.
REFRIGERATE dough, wrapped in plastic wrap, at least 2 hours or up to 2 days.
HEAT oven to 350° F. WORK with half of the dough at a time, keeping remaining dough refrigerated. ROLL out dough on lightly floured surface to 1/4-inch thickness. CUT out cookie shapes using cookie cutters; PLACE 1 inch apart on parchment paper-lined or ungreased baking sheets. BAKE until edges are lightly browned, 8 to 10 minutes. COOL on baking sheets 1 minute. REMOVE to wire racks; COOL completely.
FOR ICING: COMBINE powdered sugar, meringue powder, butter and water in mixer bowl. BEAT on high speed until light and fluffy, 6 to 8 minutes. If icing is too thick, THIN with small amounts of additional water.
Chilled dough is easier to handle and holds its shape better.
Roll the dough, cut out the shapes and put the entire baking sheet in the fridge for a few minutes before baking.
Divide icing among small bowls; tint with food coloring as desired. Ice cookies and sprinkle with colored sugars, sprinkles or nuts.