Preheat oven to 350. Place racks in upper and lower third of oven.
In a large bowl beat butter and sugar with electric mixer. Beat till light and fluffy. Beat in vanilla and salt. Turn mixer to low and gradually add flour. Beat till combined. Then, fold in pecans.
Roll dough into 1and1/2 inch balls and place on 2 baking sheets, 2 inches apart. Dampen the bottom of a glass with water and lightly flatten each ball.
Bake until cookies are golden brown, 15 to 17 minutes. Rotate pans half way through. Transfer to wire racks and let cool. Yields 18 large cookies.
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