Preheat oven to 350 F. (Not convection) Line 2 baking sheets with parchment paper.
Beat the butter and sugar together until the mixture is light and creamy, about 3-5 minutes.
Add the vanilla and beat until just mixed.
Mix the flour and ¼ teaspoon salt. Gradually add the flour to the butter mixture, mixing on low speed until the dough is just combined.
Shape the dough into a log about 2" in diameter. Wrap tightly in plastic wrap and refrigerate 1 hour until firm. (You can refrigerate for up to 24 hours.)
When ready to bake, slice the log into ¼ slices. Arrange slices on the parchment pans, leaving at least a ½" between cookies.
Sprinkle the cookies with flaky sea salt. Bake 12-15 minutes. If using 2 cookie sheets, alternate sheets halfway through baking.
Remove cookies from oven and allow to cool about 5 minutes before transferring to a wire rack to finish cooling.
Dough logs can be frozen, tightly wrapped for 3 months. Thaw and slice when ready to bake.