In a pan, heat 2 tbsp of oil over medium heat, add the mushrooms, sauté while stirring constantly for 1 to 2 minutes, until they are tender. Remove the pan and set aside. In the same pan, add 3 tbsp of oil, add the broccoli and cook while stirring constantly until tender but crisp. Add the broth to the broccoli mixture. Mix together cornstarch, salt, and cold water, and add to the broccoli mixture. Bring to a boil while stirring constantly, let simmer until thickened, add the mushrooms, and serve.