Beat butter at medium speed with electric mixer until fluffy; add 3/4 cup sugar, beating well. Add egg and next 3 ingredients, beating until blended.
Combine flour, baking soda, and salt; gradually add to butter mixture, beating until blended. Cover and chill 1 hour.
Combine nuts and 3 tablespoons sugar in a shallow bowl.
Shape dough into 1-inch balls; roll in nut mixture, and place 2 inches apart on ungreased baking sheets. Flatten slightly with hands or bottom of a glass.
Bake at 350° for 10 to 12 minutes or until golden brown. Remove to wire racks to cool.
*Fresh sweet basil may be substituted.
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