In a large bowl, cream the butter and sugar until mixed. Switch to a fork and beat the butter mixture until light and fluffy. (Use the same motion you would use for whisking scrambled eggs.)
Switch back to the spoon and beat in the eggs and vanilla. Beat in flour gradually, mixing just until dough it's combined. If your hands are clean, ditch the spoon and get in there with your fingertips!
Flatten the dough into a disc and wrap in cling wrap. Refrigerate for 2 hour.
Slice the cookie dough and place the cookie dough on the sheet pan. Since the butter cookie dough spreads out a little bit in the oven, place each cookie dough at least 1 inch apart from each other.
Bake for 10–12 minutes. Rotate the sheet pan in the middle of baking, so the cookies get brown evenly.
Let the cookies cool down on a rack.
Notes
This makes 2 lbs dough. You can make 6 dozens of butter cookies from this dough.