Combine all of the teriyaki sauce ingredients except for the tablespoon of water and cornstarch in a small saucepan over medium-high heat. Stir until the mixture begins to simmer and the honey is fully dissolved.
In a small dish, mix together the water and cornstarch to form a slurry. Add to the soy mixture and whisk until the sauce is thickened, about 1 minute. Remove from heat and set aside.
Heat 1 tablespoon of oil in a large skillet over medium-high heat. Add sliced mushrooms and onions and cook until the mushrooms have released most of their liquid and the onion is tender and beginning to caramelize, about 7-8 minutes.
Pour in the teriyaki sauce and toss to coat all the vegetables. Bring to a simmer and cook for another 1-2 minutes or until the vegetables are cooked to desired tenderness.