Prepare all the vegetables before you start cooking: thinly slice the onion, carrot, and red bell pepper; trim the snap peas; cut the broccoli into small florets; and slice the mushrooms if they are not already sliced.

In a small bowl, whisk together the soy sauce, water, and cornstarch until the cornstarch is fully dissolved, then set the sauce mixture aside.

Heat the vegetable oil in a large skillet or wok over medium-high heat until the oil is hot but not smoking.

Add the sliced onion to the pan and cook for about 2 minutes, stirring often, until it starts to soften.

Stir in the minced garlic and grated ginger, cooking for about 30 seconds until fragrant, stirring constantly to keep them from burning.

Add the broccoli florets and sliced carrot to the pan and stir fry for 3 to 4 minutes, until they begin to turn bright in color but are still crisp.

Add the red bell pepper, snap peas, and sliced mushrooms to the pan and continue to stir fry for another 3 to 4 minutes, until all the vegetables are tender-crisp.

Give the soy sauce mixture a quick stir, then pour it into the pan, stirring well to coat all the vegetables evenly.

Cook for 1 to 2 minutes, stirring frequently, until the sauce thickens slightly and clings to the vegetables.

Turn off the heat, then drizzle the sesame oil over the vegetables and sprinkle with black pepper and salt to taste, tossing gently to combine before serving.