Preheat oven to 350 degrees. Generously grease cookie sheets. Pulse 1/2 cup toasted walnuts with 1 tablespoon granulated sugar in food processor until very fine.

Combine 1/4 cup butter, cut up, 1/4 cup firmly packed brown sugar and 1/4 cup light corn syrup in medium saucepan; bring to boil, stirring. Remove from heat and stir in walnut mixture, 6 tablespoons all-purpose flour and 1/2 teaspoon vanilla.

Drop batter by level measuring teaspoonfuls 3 inches apart on prepared cookie sheets. Bake until browned, 5-7 minutes. Let stand until firm enough to remove from sheets, about 1 minute. Quickly transfer to wire racks to cool completely. If cookie sticks to sheets, return to oven 1 minute. Makes 4 dozen.