FOR THE BÉCHAMEL SAUCE:
Season the chicken with salt and pepper, and set aside.
In a medium pot over medium heat, boil the broccoli florets for 2 minutes, until they are tender. Immediately shock the broccoli by placing the florets in a bowl of ice water for 2 minutes to retain their green color. Drain and set aside to cool.
Heat the vegetable oil and butter in a large, heavy pot over medium heat. Add the diced chicken to the pot and fry the chicken until it has browned on all sides, for about 7 minutes.
Add the onion to the pot and sauté until softened, for another 7 minutes.
Add the potato, carrots, and celery and sauté for 2 minutes.
Add enough chicken or vegetable broth to cover the majority of the vegetables. Add the bay leaves and bring the stew to a boil, then cover and reduce the heat to a simmer. Cook for 8 minutes.
While the cream stew is cooking, start the béchamel sauce. In a small pot, melt the butter on medium heat. Make a roux by adding the flour, and continuously whisk until it is well incorporated 4 to 7 minutes. (The roux should bubble.)
Warm the milk in the microwave for 30 seconds to 1 minute. While continuously stirring, slowly add the warm milk to the pot until the béchamel sauce be- comes thick and creamy.
Season the sauce with salt, pepper, and nutmeg. Stir well, then set aside.
Uncover the stewpot and check the potatoes. The potatoes are fully cooked when you can insert a fork into them with ease.
Ladle about ½ cup of broth into the béchamel sauce and stir until combined. Pour the béchamel sauce into the stewpot and gently stir without breaking apart any of the vegetables.
Add the sliced mushrooms, cooked broccoli, and green peas. Simmer for an additional 3 to 5 minutes on low heat, uncovered. Season the stew with salt and pepper, to taste.
Serve the stew with steamed rice and garnish with chopped parsley.
TIP: Pour small amounts of warm milk into the roux when making your béchamel sauce to keep lumps from forming. Add ½ teaspoon garlic powder to the béchamel sauce when adding the salt, pepper, and nutmeg to the sauce for stronger flavor.
