Slice the florets off the broccoli crown and cut them down into 1 ½-inch pieces. If you rinse your broccoli, be sure to turn it out on paper towels to drain and blot it dry before adding it to the hot oil.
Before you start cooking, chop the onion, bell pepper, mushrooms, (and garlic and ginger if using fresh). Place all the ingredients within reach.
For the stir fry sauce, combine the soy sauce, rice vinegar, sesame oil, sugar, red pepper flakes, and cornstarch in a small bowl and set aside.
Heat the vegetable oil in a large nonstick skillet or wok over HIGH heat, swirling to coat the pan. When very hot, add the broccoli florets, onion, and red bell pepper. Cook, stirring constantly, until the broccoli is browned around the edges, about 2 to 3 minutes.
Add 2 tablespoons of water to steam the broccoli, and cook, stirring constantly, for about 1 minute and then add the mushrooms. Continue to cook until the broccoli is fork tender, about 2 minutes more.
Add the garlic and ginger and cook, stirring, for 1 to 2 minutes. Add the soy mixture, and stir until the sauce has thickened and the broccoli is coated, about 30 seconds. Remove from the heat. Garnish with sesame seeds (if using) and serve immediately.