Chilled Lobster Tails with Green Goddess Aioli

Name: Chilled Lobster Tails with Green Goddess Aioli
Ingredients: 1/2 cup plus 2 tablespoons mayonnaise; 1/2 cup loosely packed fresh parsley leaves; 1/2 cup loosely packed fresh basil leaves; 1 large scallion, chopped (about 3 tablespoons); 2 tablespoons fresh lemon juice (from 1 lemon); 4 oil-packed anchovy fillets (from 1 [2-ounce] can) (see Note); 1 small garlic clove , finely grated (about 1 1/2 teaspoons); Kosher salt, to taste; Black pepper, to taste; 6 (4- to 6-ounce) fresh Maine lobster tails , halved lengthwise