Gather all ingredients.
Preheat oven to 400ºF. Heat oil in a 10-inch cast-iron skillet over medium-high. Sprinkle chicken evenly with salt and pepper. Place chicken skin-side down in a single layer in skillet; cook, undisturbed, until skin is golden brown, 10 to 12 minutes. Transfer chicken to a plate skin-side up, reserving drippings in skillet; set aside. (Chicken will not be fully cooked.) Do not wipe skillet clean.
Add onions to reserved skillet; cook over medium, stirring occasionally, until softened and golden, 12 to 15 minutes. Add vinegar and cook, stirring constantly to scrape up any browned bits on bottom of skillet, until evaporated, about 1 minute.
Add broth, soup mix, and thyme to onion mixture; bring to a simmer over medium-high. Stir together cornstarch and water in a small bowl, then add to broth mixture; simmer, stirring constantly, until thickened, 1 to 2 minutes.
Remove from heat and nestle reserved chicken thighs into broth mixture, skin-side up.
Bake in preheated oven until an instant-read thermometer inserted in thickest part of chicken registers 180°F to 190ºF, 15 to 18 minutes. Serve over mashed potatoes, and garnish with thyme.
