Traditional Caesar salad dressing uses egg yolk to make it creamy. Here we use mayo instead for the same rich results without the raw egg.
Preheat grill to medium.
Whisk mayonnaise, lemon juice, oil, mustard, anchovy paste, garlic and 1/4 teaspoon pepper in a small bowl. Stir in Parmesan. Set aside.
Sprinkle both sides of steak with 1/4 teaspoon salt and the remaining 1/4 teaspoon pepper.
Oil the grill rack. Grill the steak, flipping once, until an instant-read thermometer inserted in the thickest part registers 125°F for medium-rare, about 10 minutes. Transfer to a clean cutting board and let rest for 5 minutes. Slice the steak against the grain.
Meanwhile, toss tomato, onion and the remaining pinch of salt in a medium bowl. Arrange romaine on a platter and top with the tomato mixture and the steak. Drizzle with the reserved dressing and serve with lemon wedges, if desired.