Preheat oven to 300°F (150°C). Pat chicken pieces completely dry with paper towels. Season generously on all sides with kosher salt and black pepper. Let sit at room temperature for 20 minutes.
Sear the chicken: Heat olive oil in Dutch oven over medium-high heat until shimmering. Add chicken skin-side down in a single layer (work in batches if needed). Sear without moving for 5–7 minutes until deep golden brown. Flip; sear other side for 3–4 minutes. Transfer to a plate.
Caramelize the onions: Reduce heat to medium. Add 1 tablespoon butter. Add sliced onions and a pinch of salt. Cook, stirring occasionally, for 12–15 minutes until deeply golden and caramelized.
Add aromatics: Add crushed garlic; cook 2 minutes until fragrant. Add tomato paste; stir and toast for 1–2 minutes until darkened to brick-red.
Deglaze: Pour in white wine, scraping all browned bits from the bottom. Reduce 2–3 minutes. Add Worcestershire sauce and chicken stock. Add rosemary, thyme, and bay leaves. Bring to a gentle simmer.
Add vegetables: Add carrots, parsnips, and celery. Nestle seared chicken back into pot, skin-side up. Tuck potatoes in around the chicken. Liquid should reach halfway up the chicken — not submerge it.
Braise: Cover with lid and transfer to oven. Braise for 1 hour 45 minutes to 2 hours. Remove lid in last 15 minutes and increase temperature to 400°F (200°C) to crisp the skin.
Rest: Remove from oven. Let rest, uncovered, for 10 minutes before serving.