In a large bowl, cream the butter, sugar and vanilla with an electric mixer. Add the egg and beat until smooth. With the mixer at low speed, or using a wooden spoon, stir in the dry ingredients. Shape into 2 discs. Cover with plastic wrap and refrigerate for 1 hour.
With the rack in the middle position, preheat the oven to 350°F (180°C). Line two baking sheets with parchment paper or silicone mats.
On a lightly floured surface, roll out one piece of dough at a time to a thickness of 1/4 inch (1/2 cm). Cut the cookies with a 4-inch (10 cm) holiday-themed cookie cutter. Place on the prepared sheets, spacing them evenly. Use the scraps.
Bake one sheet at a time for 12 minutes or until light golden brown. Let cool completely.
Decorate with vanilla royal icing, if desired. The cookies will keep for 3 weeks in an airtight container at room temperature.