In a small bowl, mix the beef broth, soy sauce, black bean chili sauce, and sugar, stirring until combined. Set aside.
Preheat a large skillet over medium-high heat. Add the ½ tablespoon of the olive oil and swirl the pan to coat the bottom.
Add steak slices and stir-fry for 4 minutes, until the meat just loses its pink color. Remove the steak from the skillet and cover to keep warm.
Add a the remaining olive oil to the skillet. Add the mushrooms and stir to coat, cooking over medium heat for 4 minutes, until the mushrooms have released their water and begun to brown.
Transfer the mushrooms to the same bowl as the beef and cover to keep warm.
Add the broccoli to the hot skillet along with 1-2 tablespoons of water. Cover immediately and steam for 3 minutes, , until broccoli is bright green and just tender. Transfer the broccoli to a separate bowl and keep warm.
Pour the sauce mixture into the hot skillet that you cooked all the other ingredients in. Bring the sauce mixture to a boil. In a small bowl, mix together the water and cornstarch until smooth.
Add the cornstarch slurry to the sauce mixture, whisking constantly. Bring the sauce to a boil the turn the heat down to low and cook for 2 minutes, or until the sauce begins to thicken.
Remove the skillet from the heat and add steak/mushroom mixture stirring to coat with the sauce sauce.
Add the cooked broccoli and pasta, tossing to coat well with sauce.