How to Make It
Preheat oven to 400°F.
Sprinkle chicken with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Heat 1 1/2 teaspoons oil in a 10-inch cast-iron or other ovenproof skillet over medium-high. Add chicken to pan; cook until browned on both sides, about 3 minutes per side. Transfer chicken to a plate.
Add remaining oil to pan. Add onion and garlic; cook, stirring occasionally, until lightly browned, about 5 minutes. Add bulgur and oregano; cook, stirring often, until fragrant and toasted, about 2 minutes. Add kale and bell peppers; cook, stirring constantly, until kale begins to wilt, about 2 minutes. Add stock and remaining 1/4 teaspoon each salt and black pepper; bring to a boil. Remove from heat.
Nestle chicken into bulgur mixture; place skillet in oven. Bake at 400°F until a meat thermometer inserted in thickest portion of chicken registers 165°F, 12 to 15 minutes. Remove from oven. Sprinkle with feta. Let stand 5 minutes. Sprinkle with dill, and serve immediately.