Pat the chicken pieces dry the generously season with salt & pepper. Add the flour to a shallow bowl and coat the chicken pieces in the flour and shake off any excess flour from the chicken.
Heat the oil in a large dutch oven over medium-high heat. When the oil is hot melt the butter in with the oil. When the butter is melted add the chicken pieces (in batches, dont overcrowd the pan) and cook until browned on each side, about 4 minutes per side. Transfer the browned chicken to a plate and set aside.
Keep the oil in the dutch oven over medium-high heat and add the shallots, garlic, and mushrooms to the pot. Cook, stirring occasionally, about 5 minutes.
Add the white wine and using a wooden spoon scrape the bottom of the pan to release and stuck on bits. Cook until most of the liquid in the pot has evaporated, about 5 minutes.
Stir in the chicken stock, crushed tomatoes, thyme, and ½ tsp salt. Nestle the chicken pieces back into the pot and bring the contents of the pot to a boil.
Cover the dutch oven and reduce heat to medium-low. Simmer for 20 minutes.
Uncover the dutch oven and continue simmering, stirring occasionally, until chicken is tender and the sauce has reduced a bit, about 20 more minutes.
Transfer the chicken pieces to a large serving bowl or platter. Continue to simmer the sauce to desired thickness, stir the fresh parsley into the sauce and season with salt and pepper to taste. Pour sauce over the chicken and serve.
