Preheat your oven to 325°F (160°C) and line two lightly colored baking sheets with parchment paper.

In a stand mixer, combine softened butter, powdered sugar, and vanilla extract. Mix on low speed until the mixture begins to turn crumbly.

Gradually add all-purpose flour until the dough binds together. It should be somewhat dry but easily form a ball when handled.

Roll the dough out between two sheets of parchment paper to about 1/3-1/2 inch thick, making sure it's an even thickness for uniform baking.

Use a cookie cutter to cut out small 3-inch circles, transferring them carefully to the prepared baking sheets.

Bake for 12-15 minutes, keeping an eye on them; they should be barely golden brown on the bottoms.

Allow the cookies to cool for 5 minutes on the baking trays before transferring them to cooling racks.