Preheat oven to 350°. Grease a 9-inch square baking pan with butter. Line bottom and sides with parchment paper, leaving a 1-inch overhang on all sides. Set aside.
Beat butter, flour, sugar, vanilla and salt with a stand mixer fitted with a paddle attachment on low speed until mixture is well-combined and just beginning to come together, 45 seconds to 1 minute.
Using your hands, press dough evenly into prepared pan. (If mixture is too sticky, place a sheet of parchment paper on top of dough, and press into pan. Remove parchment before baking.)
Bake until edges are golden brown, 30 to 35 minutes. Remove from oven, and cool completely in pan, about 1 hour. Using parchment paper as handles, lift biscuits from pan. Cut into 18 rectangles.
