In Large Bowl; with mixer at low speed, beat butter with sugar until blended. Increase Speed to high; beat until light & fluffy about 3 minutes. At Low speed beat in flour, vinegar, & baking soda until mixed; occasionally scraping bowl with rubber spatula. Cover bowl with plastic wrap & refrigerate dough 1 hour or until easy to handle.
Preheat Oven to 350, Drop dough by rounded teaspoons, about 2 inches apart, onto Ungreased Large cookie sheet Recipe says 17 to 20 minutes, but Check on your first batch, mine came out Much Sooner, they should only be Golden Brown at the Edges & Set, before you remove them from the cookie sheet (about 30 seconds)Remove with a pancake turner, (they are Very Thin)& onto a wire rack to Cool completely
Repeat with remaining dough. Makes about 4 dozen cookies