Yield: Makes 3 to 5 dozen cookies (depending on size of cookie cutters)
2 1/2 cups all-purpose flour
3/4 teaspoon salt
1 1/2 sticks (3/4 cup) unsalted butter, softened
3/4 cup sugar
1 large egg
1 teaspoon vanilla
Various food colorings *
Special equipment: 2- to 3-inch alphabet cookie cutters**; several sealable plastic bags (not pleated)
Whisk together flour and salt in a small bowl.
Beat together butter and sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 3 minutes in a standing mixer (preferably fitted with paddle attachment) or 6 minutes with a handheld, then beat in egg and vanilla. Reduce speed to low and add flour mixture, mixing until just combined.
Form dough into 2 balls and flatten each into a 6-inch disk. Chill disks, wrapped in plastic wrap, until firm, at least 1 hour.
Put oven rack in middle position and preheat oven to 350°F.
Roll out 1 piece of dough (keep remaining dough chilled) into an 81/2-inch round (1/4 inch thick) on a well-floured surface with a well-floured rolling pin. (If dough becomes too soft to roll out, rewrap in plastic and chill until firm.) Cut out as many cookies as possible from dough with cutters and transfer to 2 ungreased large baking sheets, arranging about 1 inch apart.
Bake cookies, 1 sheet at a time, until edges are golden, 10 to 12 minutes, then transfer with a metal spatula to racks to cool completely.
Gather scraps and chill until dough is firm enough to reroll, 10 to 15 minutes. Make more cookies with remaining dough and scraps (reroll only once) in same manner on cooled baking sheets.
For each color (you can make up to 7), transfer 1/4 cup icing to a separate small bowl and tint with food coloring. Snip off 1 corner of each plastic bag to create a 1/4-inch opening, then spoon each color icing into a bag, pressing out excess air. Twist each bag firmly just above icing, then decoratively pipe (or spread) colored icing onto cookies. Let icing dry completely (about 1 hour, depending on humidity) before storing cookies.