In a small saucepan, add broth and carrots, bring to a boil, reduce to a simmer for 5 minutes. Add the potatoes, simmer for 10 minutes. Add the peas and turn off the heat. In a skillet, add the butter, at a medium heat. Add the onion, about 4 minutes. Add the mushrooms, about 4 minutes. Preheat the oven to 425 degrees. Add the chicken, about 8 minutes. Add the vegetables, stir, maybe some corn starch to thicken.
Divided the contents of the skilllet into 3 bowls. In a mixing bowl, add the flour, butter, and milk to make into piecrust. Divide into 3 and cover the bowls. Place on a sheet in the oven for 20 minutes.