Place the potatoes in a large pot and add cold water to cover. Bring to a boil and add 2 teaspoons salt.
Reduce heat and simmer until tender, 14 to 16 minutes. Drain, run under cold water to cool, and using a fork or your fingers, break the potatoes in half.
Meanwhile, heat 1 tablespoon of the oil in a large skillet over medium-high heat. Season the steaks with 1 teaspoon salt and ¾ teaspoon pepper.
Cook steaks to the desired doneness, 4 to 5 minutes per side for medium-rare.
Meanwhile, in a large bowl, combine the blue cheese, vinegar, remaining ¼ cup oil, ½ teaspoon salt, and ¼ teaspoon pepper.
Add the potatoes and lettuce and toss to coat. Serve with the steaks.