Instead of using a cutting board -- and having to later clean it -- try this simple yet clever trick from Serious Eats: use a (very versatile) pizza cutter for in-the-bowl chopping.
The picture above pretty much says it all. Harder, small ingredients like cherry tomatoes and olives don't fare well with the pizza cutter, J. Kenji López-Alt notes, but this seems perfect for salad greens, boiled eggs, and just about anything else you would add to a salad bowl.
More details and notes in the post below.
Use a Pizza Wheel to Chop Your Salad Directly in the Bowl [Serious Eats]