For the dressing: Combine the yogurt, Parmesan, lemon juice, mustard, olive oil, oregano, anchovies, garlic, 3/4 teaspoon salt and 1 teaspoon pepper in a blender or food processor and blend until smooth. Cover and chill for at least 30 minutes. The dressing will keep for up to 3 days refrigerated.
For the steak and romaine: Prepare a grill for medium heat. Lightly oil the grill grates.
Sprinkle the steaks with salt and pepper and grill about 5 minutes per side for medium rare. Remove to a cutting board to rest for 8 minutes.
Brush the cut sides of the romaine with the olive oil and season with a pinch of salt and pepper. Grill, without turning, until lightly charred and wilted, about 2 minutes. Transfer to a serving platter. Slice the steaks and place on top of the romaine. Drizzle the dressing over top and serve.
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