Bring a saucepan of water to a boil. Add potatoes and carrots; cook until softened, about 8 minutes. Add peas; cook until tender, about 2 minutes. Drain.
Heat butter in a heavy skillet until melted. Add chicken and garlic; cook and stir until lightly browned, about 5 minutes. Stir in mushrooms and green onion; cook until softened, about 2 minutes. Stir in flour and cook for 1 minute.
Stir chicken stock, heavy cream, mustard powder, salt, and pepper into the skillet. Simmer until thickened, about 5 minutes. Fold in potatoes, carrots, and peas; cook until warmed through, about 2 minutes. Remove stew from heat and garnish with cilantro.