Preheat oven to 350º F. Line rimmed baking sheet with parchment paper or a silicon baking mat.
Cream butter and sugar together until light and fluffy, about 3 minutes. Add in vanilla and egg, making sure to combine well. Combine buttermilk and baking soda and add to mixture alternately with flour.
Lightly flour counter top and roll dough thin. Cut with cookie cutter and place onto prepared baking pan. Place in oven and bake until lightly browned, about 10 to 12 minutes.