Process all ingredients in food processor or blender until smooth, stopping to scrape down sides. Store in an airtight container in the refrigerator up to 1 week.
Garlic-Chili Mayonnaise: Omit lemon rind and basil. Substitute fresh lime juice for lemon juice. Stir together mayonnaise, juice, and 2 Tbsp. Asian garlic-chili sauce. Makes about 1 cup.