In a large wok or large skillet, heat the sesame oil over medium-high heat. Add the broccoli stir-fry mix and mushrooms. Sauté the vegetables for five minutes, until the vegetables have started to soften.
In a small bowl, whisk together the chicken broth, soy sauce, garlic, vinegar, oyster sauce, brown sugar, ginger, and cornstarch.
Add the shrimp to the vegetables and mix. Pour the sauce over the shrimp mixture to evenly cover, and stir frequently until the sauce has thickened and the shrimp are pinked and cooked through, 3 to 5 minutes.
Microwave the rice to package directions.
To serve, place 1/3 cup cooked rice in the bottom of a bowl, top with heaping 1 cup of the stir-fry mixture, and garnish with sesame seeds and green onions.