In a large bowl, add ground chicken, feta cheese, red bell pepper, mint, parsley, kosher salt, and black pepper.
Using your hands mix until thoroughly combined. Form into 4 equal sized patties.
For cooking in a skillet: Place a 12-inch skillet over medium-high heat and add 2 tablespoons olive oil. When the oil is hot, add the burgers and cook on both sides until the patties are golden in color and the meat is fully cooked, about 5 minutes per side or 165 degrees F internally.
For cooking on the grill: Preheat your grill to medium-high heat. Add your patties to the grill and cook until fully cooked and the patties are firm, about 10 minutes or 165 degrees F internally.
To assemble the burgers, add Greek yogurt sauce to the top and bottom of the bun, add the burger, greens of your choice, and a few pickled red onions.