Wash iceberg and romaine lettuces. Allowing all the water to drain completely.
Place in refrigerator to chill.
When lettuce is well-chilled, remove from refrigerator.
Split head of iceberg lettuce in half. Pull the heart of lettuce out of both halves. Breaking the heart into small pieces.
Separate the rest of the iceberg (it will break up fully when tossed).
Tear each leaf of the romaine lettuce into 3 sections.
Place both lettuces into mixing bowl.
Drain artichoke hearts in a colander. Measure and add to lettuces.
Add prepared onion and pimentos to lettuces.
Add olive oil, vinegar, salt, pepper. Toss to mix well.
Add parmigiano cheese. Toss until all is mixed completely.
Serve cold.