1. Measure the flour, baking soda and salt into a medium-sized bowl. Stir well and set aside.
2. In a large bowl, cream the butter and sugar with an electric mixer for about 1 minute. Add the egg and vanilla extract and mix until well combined.
3. Gradually add the flour mixture to the butter and sugar, mixing well after each addition. The dough should be stiff.
4. Add several drops of green food coloring. Knead the dough until the color is evenly distributed. (Make sure children wash their hands immediately after kneading--food coloring can be messy.)
5. Gather the dough into two balls, flatten into disks beginning at the edge of the dough and working toward the center. Cover with plastic and chill for at least 2 hours or overnight.
6. After the dough has chilled, place one half on a large piece of plastic wrap, cover with another piece of plastic wrap and then roll until it is 1/4-inch thick. Lift off the top sheet of plastic wrap and cut out shamrocks, beginning at the edge of the dough and working toward the center.
7. Place each shamrock on an ungreased baking sheet. Heat the oven to 350 degrees. Bake for 8 minutes or until the edges begin to lightly brown. Remove to a rack to cool. For particularly festive shamrocks, decorate them with green candies or frosting.
Makes about 34.