Heat oven to 300 degrees F.
Heat 1 teaspoon of olive oil over medium-high heat in a Dutch oven or stockpot.
Season the chicken liberally with salt and pepper.
When oil is hot, dredge each piece of chicken in the flour, shaking off excess.
Work in batches, likely 4 thighs at a time, and pan fry for 5 minutes each side until golden.
Remove chicken and set aside.
In the same pan, add the additional teaspoon of olive oil, then the onion, garlic, mushroom, and celery along with a large pinch of salt.
Cook for 5-7 minutes until soft and translucent.
Add the wine, scraping up the bottom of the pan and cook for 2-3 minutes more.
Add the stock, tomato puree, and parmesan rind if using.
Nestle in the chicken thighs, covering with the liquid, and bring to a simmer.
Cover and cook for 20-25 minutes in the oven until the chicken is fully cooked through.
Remove from the oven and serve chicken along with the sauce and top with the fresh parsley.