Pre-heat the oven to 350°F.
Sift the flour and salt together in a bowl. In another bowl, cream the butter and then add the sugar, vanilla and eggs. Beat until light and fluffy. Add the flour mixture slowly, mixing until smooth.
Drop the batter by half-teaspoonfuls onto ungreased cookie sheets, lined with parchment paper, about 3 inches apart (the cookies will spread!). Bake at 350°F for about 9-10 minutes; take out the cookies when the edges start to turn light brown. Watch carefully, because this happens quickly.
Let the cookies sit for one minute, then remove them to a wire rack to cool.
This recipe makes about eight dozen cookies, and they keep for a really long time in airtight tins.