Film the bottom of a very large kettle or Dutch oven, add butter, and cook over medium heat until butter is melted. Raise heat and brown chicken breasts on both sides; remove from kettle or Dutch oven.
Add diced onion and cook until onion is transparent. Add chicken breasts back into kettle or Dutch oven and add remaining onions, water, salt, chicken boullion, parsley, bay leaf, and thyme. Bring contents to a boil, cover, and simmer for 10 minutes.
Add potatoes, carrots, and mushrooms, raise heat to bring contents to a boil, cover, and simmer for 50 minutes.
Remove meat and vegetables to a warmed vegetable dish. Raise heat to high and boil liquid for 10 minutes. Mix cornstarch with water, stir in, and boil until sauce is glossy and slightly thickened. Add butter, stir until butter is melted, and pour sauce over the meat and vegetables.
Cut chicken breasts in half horizontally for easy serving and add salt and pepper to taste.