Place the butter, vanilla, salt, and powdered sugar in the mixing bowl of a stand mixer. Beat with the paddle attachment on low until homogenous and creamy. Do not aerate. Scrape the bowl.
Add the four all at once and beat on the lowest speed until the dough just comes together. Wrap the dough in plastic wrap and chill until firm, about 1 hour.
Cut the chilled dough in half and roll between sheets of parchemnt paper, or on lightly floured surface, until it is 1/4" thick.
Bake cookies in preheated 375° oven for 15-20 minutes. They should be golden to bring out the richest flavor. Cool completely on the pan and then store airtight.
Notes
I leave the butter out for 12-24 hours before mixing the dough. The softer it is the better!