Melt butter in a large heavy saucepan over medium heat. Add a single layer of chicken pieces and patiently brown them until they’re caramelized on all sides. Remove from the pan and rest on a plate. Repeat with any remaining chicken.

Add the onions to the fat and juices remaining in the pan; sauté until golden brown and caramelized. Add the garlic and sauté a few moments longer. Stir in the flour and then whisk in the chicken broth. Bring to a simmer whisking constantly until thickened.

Add carrots, celery, mushrooms, thyme (or rosemary) and reserved chicken and any juices from the resting plate. Season with salt and pepper. Continue cooking over medium heat until the stew returns to a simmer, then turn the heat down to low, just enough to maintain the simmer. The stew is really thick at this point. Don’t worry, it will get thinner as it continue to simmer on low heat.

Cover tightly and continue cooking for 30-40 minutes or until the chicken are cooked and vegetables are tender. Add the frozen peas and continue cooking for another 5 minutes. Stir in the cream and green onions. Correct seasonings by adding salt and pepper to taste. Serve immediately or refrigerate for 2 or 3 days then reheat when needed.