Crank up the oven to 350°F (175°C).
Heat the oil in a large pan or Dutch oven over medium-high heat. Generously season the chicken pieces with salt and pepper. Place them skin-side down in the pan and sear until the skin is irresistibly golden brown, 12 to 15 minutes. Flip and cook a few minutes more. Transfer to a plate.
Lower the heat to medium, add the leeks, and cook, stirring occasionally, until they begin to soften, about 5 minutes.
Stir in the garlic and rosemary, season well with salt and pepper, and cook a minute more.
Nestle the chicken into the gorgeous greenery in the pan.
Splash in the apple cider.
Spoon the beans around the chicken and stir into the leeks. Add some of the reserved bean liquid if the leeks aren't halfway covered with the cider.
Slide the pan into the oven and roast, uncovered, until the thighs are beautifully browned and register 165°F (74°C) on an instant-read thermometer and the beans are slightly crusted, 45 to 55 minutes. If the chicken is browning too quickly, cover the pan.
Remove the chicken from the oven and swirl in the sour cream.
Zest the lemon over the dish and carry it triumphantly to the table.