Using an electric mixer fitted with the paddle attachment (or by hand using a whisk) combine the butter, sugars, egg, and vanilla; beat until creamed, light, fluffy, and well combined.
Scrape down the sides of the bowl and add the flour, salt, and baking soda (keep the baking soda in a nice little mound rather than sprinkling it).
Form equal-sized mounds of dough, roll into balls, and flatten slightly on a baking sheet spaced at least 2 inches apart.
Refrigerate while the oven heats up.
Preheat oven to 350 degrees.
Bake for about 10 minutes, or until edges have set and tops are just set, even if slightly undercooked, pale, and glossy in the center; don’t overbake or undersides could become too browned. Cookies firm up as they cool.
Allow cookies to cool on baking sheet for about 10 minutes before serving.
Dust with sifted powdered sugar before serving.