Preheat oven to 350 degrees F.
Cut up all the vegetables (onion, peppers, garlic, mushrooms) and set aside.
Put the flour in a bowl. Sprinkle both sides of the chicken with salt and pepper and then dredge in the flour.
Heat the olive oil and butter in the Dutch oven over medium-high heat. Place the flour-covered chicken in the pot, and brown on both sides (about 2-3 minutes total).
After the chicken is browned (you'll have to do it in batches, as they won't all be able to brown at the same time), remove browned pieces to a clean plate. Pour off half of the fat from the pot and discard.
Add the vegetables, thyme, turmeric, red pepper flakes, and salt and pepper to the pot.
Stir and cook the mixture for a few minutes, until the vegetables start to soften.
Add the broth to the pot.
Stir and let the liquid bubble and reduce for a few minutes.
Add the can of tomatoes (including the juice).
Return the chicken to the pot, submerging it in the liquid and spooning some of the vegetables on top.
Place the lid on the pot, put the pot in the oven, and cook for 45 minutes.
While chicken is cooking, bring a pot of water to boil and cook the noodles to al dente, then drain.
Remove the lid and increase the oven temperature to 375 degrees. Braise for 15-20 minutes longer.
Remove the chicken from the pot and place on a plate. Remove the vegetables and place them on another plate. Set the pot on the stovetop and turn the heat to high. Cook to reduce the sauce for a few minutes.
Taste and see if more salt and pepper is needed, and then serve!