Using an electric mixer on medium speed, beat butter, powdered sugar, and vanilla extract in a large bowl until it just becomes light and fluffy, about 1 minute.
Add flour and on low speed, beat until the dough just starts to come together, about 3 minutes.
Turn dough out onto a lightly floured surface and press together to form a log. Divide the dough in half and form each piece of dough into a 6-inch log. Wrap in parchment paper and chill for at least 2 hours, up to three days.
Preheat oven to 350 degrees and line two baking sheets with parchment paper. Slice each log into ¼-3/4 inch slices and evenly space on the baking sheets. You should have about 40 cookies.
Bake until the bottom edges of the cookies just start to brown, 14-16 minutes. Allow cookies to cool and serve!