Season the chicken with the salt and black pepper, reserving 1/4 teaspoon of each to season the vegetables.
Dredge each piece of chicken in the flour, shaking off any excess.
In a 6 quart saute pan over medium heat, add the avocado oil and butter. Allow the butter to melt, ensuring that it does not brown or burn.Note: Adjust the heat if the butter is starting to brown before it melts. Add the chicken in a single layer and cook 4 minutes, until lightly brown. Use a tong to turn over the chicken and cook 4 more minutes. Remove from pan and set aside.Note: If using a smaller pan, brown the chicken in 2 batches. Add the onions, carrots, and peppers. Saute 5 minutes until onions and vegetables starts to soften.
Season with a pinch of the remaining salt and pepper. Stir.
Add the garlic, herbs and capers. Stir. Add the diced/chopped tomatoes. Season with remaining salt and pepper. Stir. Cook 3 to 4 minutes with heat turned up to medium high.
Add the chicken broth. Stir. With heat at medium, cook 10 to 15 minutes until tomatoes start to break down.
Add the canned tomatoes. Bring to a boil.Add the chicken parts in a single layer. Cover and simmer 30 minutes.
Uncover, and flip the chicken parts over. Cover and continue simmering until chicken is very tender - 15 to 20 minutes.
Garnish with scallions or herbs of choice. Plate and serve with your favorite side dish. I usually serve this with pasta, but rice will do.
Enjoy.