In a small bowl, soak black mushrooms in hot water for 15 minutes. Drain well in a colander and shred, discarding the stems.
In another small bowl, stir together cornstarch and broth. Set aside.
In a large skillet or wok, heat 2 tablespoons oil over high heat for 1 minute. Add meat and cook, stirring constantly, for 2 to 3 minutes, or until beef is tender and nearly all brown. Place meat in a bowl and set aside.
Wash skillet or wok and dry thoroughly. Heat 1 tablespoon oil in wok over high heat for 1 minute. Add onion and garlic and cook, stirring constantly, for 2 minutes until nearly tender.
Add broccoli and stir well. Stir cornstarch-broth mixture and add to vegetables. Cover, reduce heat to low, and simmer for 2 to 3 minutes, or until broccoli is crisp-tender.
Add mushrooms, soy sauce, fish sauce, pepper, and meat. Cook, stirring frequently, for 1 to 2 minutes, or until heated through.
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