Fill a saucepan with 4 inches of water and bring to a boil.
Place 1 egg on a spoon and lower it into the water. Repeat with the remaining eggs. Return to a boil. Cook to the desired doneness, about 6 minutes for runny yolks. Using a slotted spoon, transfer the eggs to a bowl.
In a small bowl, whisk together the vinegar, mustard, 1/4 teaspoon of the salt, 1/4 teaspoon of the pepper, 3 tablespoons of the oil, and the anchovies (if using); set aside.
Heat the remaining oil in a large skillet over medium heat. Add the garlic and cook until golden, about 1 minute. Using a slotted spoon, transfer the garlic to a plate. Add the bread sticks to the oil and cook, turning, until golden.
Divide the frisée or greens among individual plates and sprinkle with the garlic and croutons. Crack the eggs, break them in half, and use a spoon to scoop the eggs from the shells onto the salad. Top with the vinaigrette and the remaining salt and pepper.