Heat oven to 500 degrees and set a large (18- by 12-inch) rimmed baking sheet into the preheating oven. Prepare vegetables and onion. Mix soy, sherry, honey, garlic, and ginger and oil in a large bowl. Add vegetables and toss to coat, breaking up onions (and cabbage, if using).
Remove baking sheet from the oven and dump the vegetables into the hot pan, shaking to spread evenly. Immediately return pan to the oven and roast until vegetables are crisp-tender, about 7 minutes. While vegetables cook, prepare Flavoring Sauce and mix cornstarch and water.
Remove pan of vegetables from the oven. Working quickly, add peas or edamame to the pan and pour sauce over the vegetables; stir to coat. Drizzle cornstarch mixture over the vegetables; stir to coat again. Return pan of vegetables to the oven and continue to cook until sauce is bubbly and thickened slightly, about 5 minutes longer. Remove from oven; stir to coat vegetables with sauce and serve.