Heat oil in a large skillet over medium-high heat. Add onion and garlic; cook and stir until onion is translucent, about 5 minutes. Add broccoli, bell pepper, and mushrooms; cook and stir until vegetables are tender-crisp, about 5 minutes more.
Stir teriyaki sauce and cornstarch together in a small bowl; pour into the skillet. Cook and stir until sauce thickens, 1 to 2 minutes.