Trim the florets off the broccoli, and cut into 1 1/2-inch pieces. Peel the broccoli stalks with a vegetable peeler to remove the tough outer skin, and slice 1/4 inch thick on the diagonal. Set aside.
Mix 1/2 cup water, soy sauce, cornstarch, and honey in a small bowl. Set aside.
Heat a large wok over high heat. Add 2 tablespoons of vegetable oil and swirl to coat the wok.
Once the oil begins to smoke, add the broccoli florets and stems. Cook, stirring constantly, until browned around the edges, about 2 minutes.
Add 2 tablespoons of water to steam the broccoli, and cook, stirring constantly, until tender, about 2 minutes.
Push the broccoli to one side of the wok, forming an empty side.
Add the remaining 1 tablespoon vegetable oil, garlic, ginger, and pepper flakes, and stir until aromatic, 30 to 45 seconds.
Add the soy honey mixture and stir until the sauce has slightly thickened and the broccoli is coated about 30 seconds.
Remove from the heat, add the sesame oil, and stir to coat and top with crushed cashews or peanuts.
Serve as a side or pair with rice.