I got this recipe from The Joy of Baking. I did't have enoug hbutter in the house so I substituted a bit for shortening. It definitely changed the taste but they were still great! There's video here of them making the cookies and frosting them.
Sugar Cookies
Yeilds 30-40 cookies
3 cups (390 grams) all purpose flour
1/2 teaspoon salt
1 teaspoon baking soda
1 cup (227 grams) unsalted butter; at room temperature
1 cup (200 grams) granulated white sugar
2 large eggs
2 teaspoons pure vanilla extract
1. In a separate bowl whisk together the flour, salt, and baking soda.
2. In the bowl of your electric mixer (or with a hand mixer), beat the butter and sugar until light and fluffy (about 3 minutes).
3. Add the eggs and vanilla extract and beat until combined. Add the flour mixture and beat until you have a smooth dough.
4. Divide the dough in half and wrap each half in plastic wrap. Refrigerate for about one hour or until firm enough to roll.
5. Remove one half of the chilled dough from the refrigerator and, on a lightly floured surface, roll out the dough to a thickness of 1/4 inch (1 cm). (Keep turning the dough as you roll, making sure the dough does not stick to the counter.)
6. Cut out desired shapes using a lightly floured cookie cutter and transfer cookies to baking sheet.
7. Place the baking sheets with the unbaked cookies in the refrigerator for about 15 minutes to chill the dough which prevents the cookies from spreading and losing their shape while baking. (Note: If you are not going to frost the baked cookies, you can sprinkle the unbaked cookies with sparkling sugar)
8. Bake cookies for about 8-10 minutes (depending on size) or until the edges are just starting to brown.
9. Remove from oven and let cookies cool on baking sheet for a few minutes before transferring to a wire rack to finish cooling.
10. Frost with royal icing, if desired. Be sure to let the royal icing dry completely before storing. (This may take several hours or overnight.)
Royal Icing
2 large (60 grams) egg whites
2 teaspoons fresh lemon juice
3 cups (330 grams) confectioners (powdered or icing) sugar, sifted
1. In the bowl of your electric mixer (or with a hand mixer), beat the egg whites with the lemon juice.
2. Add the sifted sugar and beat on low speed until smooth.
3. If necessary, to get the right consistency, add more sugar or water.
4. Add food coloring, if desired. The icing needs to be used immediately or put in an airtight container as it hardens when exposed to air.