In a small bowl, make a slurry by mixing together the cornstarch with 1 to 2 tbsp water. The mixture should be slightly thick, but not paste. Adjust with a little more cornstarch (or water), if necessary.
2 tbsp cornstarch
Heat the peanut oil over high heat in your wok or large skillet.
2 tbsp peanut oil
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.
4 cloves garlic, 1 tbsp ginger
Add the broccoli and shallots and stir-fry for 1 minute.
6 oz broccoli florets, 1 medium shallot
Add the stock, reserved wine, ½ teaspoon salt, and cornstarch slurry. Stir to combine.
¼ cup chicken stock
Return the chicken to the pan, add the mushrooms, and stir-fry for another minute or so until the sauce thickens somewhat.
1 15 oz. can straw mushrooms
Serve immediately over rice (or noodles), and garnish with the basil, if using, and soy sauce passed at the table.
½ cup Thai basil leaves, 3 cups steamed white rice