Heat 2 tablespoons of olive oil in a large, shallow pan over high heat.
Season the chicken with salt and brown on both sides, working in batches if needed. Remove to a plate and discard most of the excess fat.
Add the remaining tablespoon of olive oil to the pan. Add the onions sweat over low heat, 8 to 10 minutes.
Add the garlic and cook for another minute.
Add the peppers, and cook until softened, about 2 to 3 minutes.
Add the mushrooms, season with salt and pepper, and cook until soft.
Add the white wine and reduce by half.
Add the tomatoes and return the chicken to the pan. Taste for seasoning. Add the red pepper flakes, parsley, bay leaves, and olives. Bring to a boil and reduce the heat to a simmer.
Partially cover the pot and simmer for 20 to 30 minutes. Check the sauce periodically and if it reduces below the chicken, replenish with water as needed.
Remove the chicken from the pot and place it on a serving platter. Taste the sauce for seasoning and add salt if needed. Discard the bay leaves.
If the sauce looks greasy, skim the surface before serving. Spoon the sauce over the chicken to serve.
Notes
To Slow Cook
Follow the recipe through step 8 then transfer to a slow cooker, cover and cook on low for 6 to 8 hours or on high for 3 to 4 hours, until chicken is cooked through.