Place a large bowl on a folded damp kitchen towel to keep the bowl from slipping.
Vigorously whisk yolks, vinegar, lemon juice, mustard, salt, pepper, and 1 Tbsp. water in a bowl to blend.
While whisking continuously, slowly add oil drop by drop to form an emulsion.
Continue whisking, slowly adding the remaining oil, until mayonnaise is smooth and creamy.
Fold in garlic, chives, parsley, and tarragon.
Season to taste with salt, pepper, and more lemon juice, if desired.