In a food processor, lightly pulse until chopped: black olives, peppers, artichokes, capers, garlic, basil, thyme and oregano. Add salt to taste.  

With food processor on, gradually add oil. Pulse lightly.

Rinse and chop green onions (not too fine).

Cut chicken into bite-size pieces, trim fat if using thighs.

Spray a non-stick skillet with oil from oil sprayer. Heat on medium high heat.

Add chicken pieces, sprinkle with kosher salt and freshly ground pepper. Cook until done, mostly no longer pink about 165°. Drain well.

In a large bowl, combine, chicken, olive mixture, mayonnaise, green onions, and cheeses. 

Preheat air fryer to 425° if you have a Breville Smart Oven Air. If you have a different fryer, start with 395°, fry a small batch and see how that works. If you want to bake them in the oven, see notes below. 

Place an egg roll wrapper on a cutting board or flat surface with one of the points facing you. (Refer to pictures in post to see how to roll/wrap them.)

Add about 1/4 cup of chicken mixture.

Roll up about 1/2 halfway, fold edges in.

Place a dab of water on the top point.  Finish rolling up egg roll. Dab a little water on the outside point so that it sticks to the egg roll.

Spray air fry basket with oil. Place egg rolls in basket, spray with oil, turn over and spray again.

Air fry for about 8-11 minutes depending on your air fryer.  With my Breville Smart Oven Air, I can do the egg rolls in 2 batches and I don't have to turn them halfway through. It takes mine about 11 minutes total. On other air fryers, watch them and adjust the time if needed. Turn them halfway through baking.

Enjoy! Dip in a good quality balsamic vinegar.