In a stand mixer, beat butter, powdered sugar and vanilla until combined. Add flour and continue mixing until it forms a dough. If dough is crumbly, mix in another 1-2 Tbsp of butter.
Form dough into a ball. Place on floured surface and roll into a tube approximately 2" in diameter and 12" long. Cover in plastic wrap and refrigerate for at least an hour, or overnight.
When ready to bake, preheat over to 350, at least 30 minutes prior to baking.
Unwrap dough and using a tape measure mark dough every centimeter. Cut at marking into discs and place on parchment lined cookie sheets.
Bake approximately 15 minutes. Start checking the oven at 12 minutes until dough sets and bottom on cookies is light golden brown. Tops should not brown.
Remove from oven onto cooling racks until completely cooled. At least 30 minutes.