In a blender, or food processor, puree the 6 anchovy fillets. Add the garlic and pulse until the mixture is well blended.
Add the egg yolks and blend the mixture for about 2 minutes. Turn off the motor, add the vinegar and lemon juice, and pulse for another 30 seconds.
With the motor running, add the olive oil in a slow, steady stream until it is incorporated.
Add the cheese, parsley, and oregano and pulse the mixture for 10 seconds.
Season the dressing to taste with a pinch of salt and pepper. Transfer to a glass or container with a tight fitting lid, and refrigerate for at least 4 hours and up to 24 hours. Chilling the dressing thickens it, and the thicker it gets, the better it sticks to the lettuce.