1. Heat oven to 350˚. Heat oil in Dutch oven or 3-qt braising pan over medium-high heat. Season chicken with salt and pepper. Cook chicken in batches until browned, 5-6 minutes per side. Remove from pot and transfer to plate.
2. Using the accumulated oil, sear the quartered mushrooms until browned all over (seasoning with salt and pepper as they cook), about 5-7 minutes. Remove from pot.
3. Using extra oil if necessary, sear squash-moons until browned on both sides (seasoning with salt and pepper while they cook), about 5 minutes. Remove from pot.
4. Using extra oil if necessary, sear turnip pieces until browned on both sides (seasoning with salt and pepper while they cook), about 2-3 minutes. Remove from pot.
5. Add celery, onion, carrot, and garlic to pot, sauté until onion is translucent, 5-7 minutes.
6. Add anchovy fillets to mire poix in pan and break apart until they disappear while sautéing.
7. Return mushrooms, squash, and turnips to pan, stir to combine.
8. Add wine and tarragon bundle and cook over high heat until reduced by half, 10-5 minutes.
9. Return chicken legs to pan, nestling them in amidst the vegetables.
10. Add enough chicken stock to the pan to come up about halfway the side of the chicken legs. Agitate the pan to mix all the ingredients.
11. Bring pan to gentle boil, cover with a lid partially on, then slide into the oven and bake for 45-60 minutes, until the chicken is tender.
12. Remove pan from the oven and take chicken legs and most of the veggies out of the sauce. Cook remaining sauce on high to reduce, adding a few pats of butter and a squeeze of lemon or a splash of sherry vinegar to enrich the sauce (optional).
13. Pour sauce over chicken and veggies on platter, garnish with celery leaves, and/or parsley serve.