Preheat oven to 350°.
Using an electric mixer on medium-high speed, beat butter and sugar until fluffy (about 3-4 minutes). Beat in vanilla and salt. With mixer speed on low, gradually add flour and beat just until combined. Fold in pecans.
Roll dough into 1 & 1/2-inch balls. Place about 2 inches apart on lined baking sheets. Lightly flatten each with the bottom of a dampened glass.
Bake cookies until golden brown (about 15-17 minutes). Cool completely on wire racks.
Makes about 18 cookies.