Make the dressing: In a small bowl or jar, whisk together olive oil, red wine vinegar, lemon juice, Dijon, garlic, oregano, basil, red pepper flakes, salt, and pepper. Taste and adjust seasoning.
It should taste bright and slightly tangy.
Prep the chicken: Shred or chop cooked chicken into bite-size pieces. If using rotisserie, remove skin and bones, and roughly chop the meat.
Chop the veggies: Halve the tomatoes, dice the cucumber and red bell pepper, and thinly slice the red onion. Slice the olives and pepperoncini.
Toss the salad: In a large bowl, combine chicken, tomatoes, cucumber, red bell pepper, red onion, olives, pepperoncini, and parsley.
Add the dressing: Pour the dressing over the salad and toss gently until everything is evenly coated.
Start with most of the dressing and add more if needed.
Finish with cheese: Fold in the Parmesan. If using avocado, add it now and gently toss again.
Rest briefly: Let the salad sit for 5–10 minutes so the flavors meld. Taste and adjust salt, pepper, or acid (a splash more vinegar or lemon, if needed).
Serve: Enjoy it as-is, or spoon it over crisp romaine or mixed greens.
It’s also great in lettuce cups.