In a large bowl, combine all ingredients for the chicken burgers except the avocado oil and mix thoroughly. Form the mixture into 4-6 evenly sized patties, depending on your size preferences.
Heat a large skillet over medium-hot heat. Drizzle the pan with avocado oil. In batches, cook the chicken burgers for 5-7 minutes per side, or until the internal temperature reaches 165 F.
For the Yogurt Sauce
In a bowl, combine the yogurt, cucumber, lemon, red wine vinegar, olive oil, salt, pepper, and fresh dill. Stir to combine.
To Assemble
Layer the burgers on top of a bed of spring mix with chopped tomatoes, sliced cucumber, sliced pepper, and olives.
Place a dollop of the yogurt sauce on top of each burger. Sprinkle feta cheese and more fresh dill onto each bowl. Serve alongside rice, quinoa, or baked sweet potato, if desired.