Add the lettuce to a cutting board. Top the lettuce with the turkey, cheese, red onion, and banana peppers.
Use a sharp knife to cut everything into small bite-size pieces.
Add the mayonnaise, red wine vinegar, oregano, salt, and pepper. Combine all of the ingredients.
Open the hot dog buns and add them to a baking sheet. Spray with olive oil spray. Place under the broiler until toasted (about 3-4 minutes).
Fill each of the hot dog buns with the turkey mixture.