Step 1

Using electric mixer, beat butter and sugar in large bowl until fluffy. Beat in egg and vanilla. Sift flour, baking powder, salt and nutmeg over; stir to blend well. Turn dough out onto lightly floured surface and knead gently 1 minute. Shape dough into 1/2-inch-thick rectangle. Cut into 4 equal pieces; wrap in plastic and refrigerate at least 3 hours and up to 1 day. Let dough soften slightly at room temperature before rolling out.

Step 2

Position rack in center of oven and preheat to 350°F. Butter large baking sheet. Working with 1 dough piece at a time, roll out dough on lightly floured surface to 1/8-inch thickness, lifting and turning dough often and dusting surface very lightly with flour to prevent sticking. Using floured 3- to 4-inch cutters, cut out cookies. Pull away excess dough from around cookies. Transfer cookies to prepared baking sheet, spacing 1 inch apart (cookies will not spread). If using cookies as hanging ornaments, push 1 end of drinking straw through dough near top of each cookie; lift straw, then remove small dough round from straw. Gently reroll dough scraps; cut out more cookies. Transfer to same sheet.

Step 3

Bake cookies until light brown, about 11 minutes. Let cool 5 minutes on sheet. Transfer cookies to rack; cool.

Step 4

Repeat with remaining dough pieces, baking 1 sheet of cookies at a time. Cool baking sheet completely and butter sheet lightly between batches.

Step 5

Whisk 9 cups sugar and powdered egg whites in large bowl to blend. Whisk in 12 tablespoons water. If necessary, whisk in more water by teaspoonfuls or more sugar by tablespoonfuls until frosting is medium-thick and very smooth. Place 1/2 cup frosting into each of 4 small bowls; mix colors using instructions in box on previous page. (Can be prepared 1 day ahead. Cover bowls and remaining frosting with plastic wrap to keep frosting from drying out. Store at room temperature.) Thin frosting in each bowl as needed by mixing in 1/4 teaspoon water at a time.

Step 6

Using pastry brush or small metal offset spatula, spread frosting on cookies; set cookies aside and let frosting dry, about 30 minutes. Cut off small tip from end of 1 disposable pastry bag (cut off slightly more if planning to insert metal tip). Fold down top 2 inches of bag, forming collar. Holding bag under collar and using small rubber spatula, fill bag with 1 color of frosting. Repeat with remaining pastry bags, filling each with 1 color of frosting. Pipe decorations onto frosted cookies in desired patterns and colors. Let cookies stand until decorations are firm and dry, at least 4 hours. (Can be prepared 3 days ahead. Place cookies in single layer between sheets of waxed paper in airtight container; store at room temperature.)