Using a stand mixer, beat the butter, powdered sugar and vanilla extract until fluffy. Use medium to medium high speed for 2 to 3 minutes.
Add the flour. Mix on low speed until the flour begins to combine, then raise to a medium-low speed until flour is incorporated and the dough begins to form a clump around the mixer paddle. Do not over mix.
Remove the dough from the bowl. Divide into 4 equal sections. Using a flat surface or cutting board, roll each section into a log a little larger in diameter than a quarter. Start by using your hands to shape some dough into a loaf shape. Use one hand to roll the loaf across the board, pick it up and place it back on the other end and roll across the board again. Keep doing this four or five times until you have a nice log. Repeat with the other 3 pieces of dough.
Wrap each log in parchment, wax paper or plastic wrap and refrigerate for at least 4 hours but ideally overnight.
Preheat oven to 350℉. Remove the cookie dough logs from the refrigerator and allow to sit at room temperature while oven preheats. Slice each log into 1/2" pieces and place on a baking tray lined with parchment paper. Bake for 12-14 minutes until just barely beginning to brown on the edges. Better to under do it than over do it. Remove from oven and cool before storing.