Arrange a rack in the middle of the oven and heat the oven to 400ºF. Halve 1 medium yellow onion, then cut into 1-inch thick wedges.
Season 4 bone-in, skin-on chicken thighs with 1 teaspoon kosher salt. Place skin-side down in an unheated large cast iron skillet. Place over medium-high heat and sear undisturbed until the chicken skin is golden brown and releases easily from the pan, about 10 minutes.
Flip the chicken and sear until browned on the second side, about 5 minutes. Meanwhile, place ½ cup mayonnaise in a small bowl, add 1 envelope onion soup mix, and stir to combine.
Transfer the chicken to a plate. Add the onion wedges to the pan and cook, trying to keep them intact as much as possible, until light golden brown on both sides, about 2 ½ minutes per side.
Add 2 tablespoons of the apple cider vinegar and 1 teaspoon chicken bouillon paste and scrape up any browned bits from the bottom of the pan with a wooden spoon. Turn off the heat.
Dollop 1 tablespoon of the mayonnaise mixture onto each piece of chicken and spread all over with the back of a spoon. Return the chicken skin-side up to the pan, moving the onions around as needed so they aren’t covered by the chicken.
Transfer the pan to the oven and roast until the internal temperature of the thickest part of the chicken not touching bone registers at least 165ºF on an instant-read thermometer, about 20 minutes. Meanwhile, finely chop 1 medium bunch fresh chives until you have 3 tablespoons. Add 2 tablespoons of the chives and ½ cup Greek yogurt to the remaining mayonnaise mixture and stir to combine.
When the chicken is ready, if you’d like a bit more color and crunch, turn the oven to broil and broil until well browned and the skin is crisp, about 2 minutes.
Transfer the chicken to a plate. Add the remaining 1 tablespoon apple cider vinegar and ½ teaspoon black pepper to the pan and scrape up the browned bits from the bottom with the wooden spoon.
Spread the yogurt mixture onto a large plate. Top the yogurt mixture with the onions and chicken. Pour the drippings in the pan over the chicken. Sprinkle with the remaining 1 tablespoon chives.
