In a wok (or large skillet), heat the peanut oil over high heat.
Add the chicken and stir-fry, until starting to brown, about 3 minutes.
Transfer the chicken to a bowl (don't worry, you're not done cooking it yet).
Add the garlic, ginger, and black beans to the wok and stir-fry until fragrant, about 30 seconds.
Add the broccoli and shallots and stir-fry for 1 minute.
Add the stock, reserved sherry, and 1/2 teaspoon salt and stir to combine.
Return the chicken to the pan, add the mushrooms, and stir-fry until most of the liquid has evaporated, about 3 minutes.
Serve over noodles or rice (if using), and garnish with the basil.