Process mayonnaise and garlic clove in a food processor until smooth. Add basil leaves and lemon rind; pulse 3 to 4 times or until basil is finely chopped. Store in refrigerator up to 1 week.
Even though this won't freeze, it's unbelievably delicious with a bowl of grape tomatoes or on a turkey sandwich. Use it in place of plain mayonnaise in deviled eggs or main dish salads; it's also great with chicken, shrimp, or tuna. Try this flavorful mayonnaise instead of tartar sauce the next time you serve your favorite fish.