Whip butter with sugar until soft and fluffy. Add egg and vanilla and beat until mixed.
Place flour in a large bowl and make a well in the center. Place butter and sugar mixture in the well and start working with fingers just until ingredients get together and form a soft dough. Do not overwork dough. Divide dough in half and wrap in plastic film.
Refrigerate 30 minutes.
Flour the working surface and roll out first half of dough with a floured rolling pin. Cut 2 ½ inch circles (5 cm) and carefully place them on an ungreased cookie sheet. Have 1 ½ inch (3 cm) separation between cookies.
Bake cookies in a preheated moderate oven at 350°F (180°C) for 12 – 15 minutes. Remove from oven and set aside for 1 minute. Transfer cookies to a rack and cool completely. Keep in an airtight container.