In a food processor, or blender, add ½ the seeded and diced cucumber, plain Greek yogurt, olive oil, minced garlic, fresh dill, fresh lemon juice, salt, pepper, garlic powder, and onion powder. Process until semi-smooth.
Pour mixture into a large bowl and add mayonnaise. Mix until combined. Cover and chill, until ready to use.
Butterfly and tenderize two boneless chicken breasts. Cut into four pieces. Place chicken in a large Ziploc bag and add Greek Salad dressing. Marinade for a minimum of 30 minutes, up to 24 hours in the refrigerator.
Preheat the BBQ grill, or stove top skillet, to medium-high heat. Place marinated chicken on preheat grill. Grill each side 6 - 8 minutes or until juices run clear. Remove from heat.
Toast buns if desired.
Spread dill sauce on the bottom of the bun. Top with 1 - 2 Tablespoons of Feta cheese. Add a handful of spring mix. Top with a piece of grilled chicken. On top of the chicken place 1 - 2 slices of tomato, and sliced onions. Spread the inside top of the bun with more dill sauce. Add thin slices of cucumber. Bring two halves together, top and bottom, and serve while warm.