In a medium bowl, whisk together ½ cup oil, 2 tablespoons Dijon, 2 tablespoons dill, zest of 1 lemon, 1 tablespoon lemon juice, 1 tablespoon red wine vinegar, grated garlic, sugar, ½ teaspoon salt, and ½ teaspoon onion powder. Transfer 5 tablespoons of marinade to a large mixing bowl; cover and refrigerate the rest until ready to serve.

Cut each chicken breast in half crosswise to create two halves, one that’s naturally thicker and one that’s naturally thinner. Slice thicker halves in half horizontally to create two thinner halves. Using the heel of your hand, firmly press all six chicken pieces (3-4 ounces each) into an even ¼-inch thickness.

Add chicken to bowl with the 5 tablespoons marinade; season with ½ teaspoon salt and pepper, toss to coat then cover and refrigerate 2–8 hours.

Preheat a 12-inch skillet over medium heat. Add ½ tablespoon butter and ½ tablespoon vegetable oil; swirl to melt.

Add chicken pieces in an even layer (don’t overcrowd the pan, you’ll be cooking the chicken in batches) and cook until bottom sides are golden brown, about 3 minutes. Flip and continue to cook until second side is golden brown and an instant-read thermometer inserted in the centers registers 163–165ºF, 3–4 minutes more (the smaller pieces will likely be done first, pull them as they come to temperature and are finished cooking). Transfer chicken pieces to a plate and set aside. Repeat process with remaining chicken.

Slice and serve chicken with rice, lettuce, tomatoes, cucumber, feta, pickled onions, and olives; drizzle each serving reserved marinade.