In large bowl, beat granulated sugar, brown sugar, butter, vanilla and eggs with electric mixer on medium speed until well blended, scraping bowl occasionally. On low speed, beat in flour, baking powder and salt until well combined, scraping bowl occasionally. Stir in nuts.
Divide dough into 3 equal parts; shape each into roll 1 1/2 inches in diameter. Wrap each roll in plastic wrap; refrigerate until firm, about 2 hours.
Heat oven to 425°F. Cut dough into 1/4-inch slices; place 1 inch apart on ungreased cookie sheets.
Bake 5 to 7 minutes or until light golden brown. Immediately remove from cookie sheets.