Preheat the oven to 425°F (220°C). Line a large sheet pan with parchment paper or lightly grease it.
In a large bowl, combine the red bell pepper, yellow bell pepper, zucchini, red onion, broccoli florets, and halved mushrooms.
Drizzle the olive oil over the vegetables and sprinkle with salt and black pepper. Toss well to coat evenly.
Spread the vegetables in a single layer on the prepared sheet pan.
Roast the vegetables in the preheated oven for 20 minutes, stirring halfway through to ensure even cooking.
While the vegetables roast, prepare the teriyaki sauce. In a small saucepan, whisk together the soy sauce, honey, rice vinegar, water, grated ginger, and minced garlic.
Place the saucepan over medium heat and bring the mixture to a gentle simmer.
In a small bowl, mix the cornstarch with 1 tablespoon of cold water to create a slurry.
Slowly whisk the cornstarch slurry into the simmering sauce. Continue to cook, stirring constantly, until the sauce thickens, about 1-2 minutes.
Remove the sauce from heat and set aside.
After 20 minutes of roasting, remove the vegetables from the oven and drizzle the teriyaki sauce evenly over them.
Toss the vegetables gently to coat them with the sauce, then spread them back out on the sheet pan.
Return the sheet pan to the oven and roast for an additional 5 minutes to allow the sauce to caramelize slightly.
Remove from oven and serve warm.