1. Combine butter and 1/2 cup sugar, stir well. Add eggs and beat by hand. Add lemon zest, lemon juice, and fresh basil. Mix together. Add flour, baking soda, and salt to egg mixture and mix by hand.
2. Cover and chill 1-2 hours (or up to 2 days). Preheat to 350F. Combine pistachios and remaining 1/2 cup sugar.
3. Scoop dough into 1 1/2 inch balls and roll in pistachio sugar mixture. Place on cookie sheets and flatten each with the bottom of a glass. Bake for 10-12 minutes. Makes 3 to 4 dozen.