Put the eggs in a pot and fill with cold water to cover. Bring the water to a boil, covered, then shut off the heat and wait 5 to 6 minutes, depending on the size of your eggs. Run under cold water or dunk in ice water.
Peel and halve them, vertically, and scoop the yolks into a bowl.
Roughly chop the garlic and smash it to a paste with a small pinch of salt in a mortar or on a cutting board. Finely chop the anchovies and mix well with the garlic. Add to the yolks along with the Parmesan, olive oil, lemon juice, and vinegar. Add the salt and freshly ground black pepper, and mix. Taste and adjust. Add the romaine, mix well, and using a small spoon, fill the waiting egg whites with the mixture. These can be chilled for a few hours. Bring to room temperature for 15 minutes before serving.