How to Make It
Preheat oven to 450°F. Heat 1 tablespoon of the oil in a large cast-iron skillet over medium-high. Sprinkle chicken on all sides with 3/4 teaspoon of the salt and 1/2 teaspoon of the pepper. Place chicken in skillet, skin side down; cook, undisturbed, until brown and crispy, about 8 minutes. Flip, and continue to cook until browned on other side, about 4 minutes. Transfer chicken to a plate. (Chicken will not be cooked through.)
Place onion slices in skillet in a single layer over medium-high; cook, undisturbed, until slightly charred, 4 to 6 minutes. Flip, and cook until charred on other side, about 2 minutes. Transfer to plate with chicken.
Add tomatoes and remaining 1 tablespoon oil to skillet; cook, undisturbed, until blistered, about 4 minutes. Add green beans, garlic, capers, and oregano; cook until fragrant, about 1 minute. Sprinkle with remaining 1/2 teaspoon each salt and pepper. Stir in white wine. Place charred onions on top of tomato mixture; nestle chicken into tomato mixture.
Bake in preheated oven until a thermometer inserted in thickest portion of chicken reaches 170°F, 12 to 15 minutes. Remove from oven, and garnish with oregano.