Toss together the olive oil, potatoes, salt, and pepper in a medium bowl.
Tossing 2 tbsp olive oil, the chicken breasts, dried oregano, smoked paprika, shallot, garlic, salt, pepper, and chili flakes in a large bowl.
Rub all slides of chicken breasts thoroughly.
Place the 2 lemon slices first if you are using them, and then place the butter pieces on each chicken breast.
Select Roast, set the temperature to 385 °F, and the timer to 20 min. Press Start.
Once the air fryer is preheated, open the air fryer basket, and place the two chicken breasts and the potatoes carefully into the basket. Close the basket.
Meanwhile, add extra virgin olive oil, parsley, oregano, dill, red wine vinegar, roasted red pepper, Greek olive mix, salt, and pepper in a bowl.
Once the cooking cycle is done, open the basket and check the temperature of the chicken breasts with a thermometer to ensure they reach 165 °F. Once the chicken breasts get higher than 165 °F, remove the chicken breasts and potatoes and place them evenly on each serving plate.
Break the feta over the chicken, and then add the dressing.