Trim the dry ends off the sprouts and then cut them in half. Prepare the remaining vegetables and heat a non-stick skillet. Have the vegetable broth standing by.
Put the onions into the hot skillet and give them a sprinkle of salt (optional, but speeds browning). Stirring constantly, adding a teaspoon or two of broth to the skillet if the onions stick, cook until the onions begin to brown, about 2-3 minutes. Add the garlic and more broth if necessary, and cook for another minute. Remove onions and garlic to a plate and return the skillet to the heat.
Put the sprouts into the skillet, cut side down. Cook until they begin to brown and then add in the mushrooms and stir. Cook for another minute or two, stirring frequently. Add about 1/2 cup vegetable broth and the reserved onions, stir, turn down the heat, and cover tightly. Cook until the sprouts are tender and easily pierced with a fork, 3-5 minutes, adding more broth if necessary. Season with salt and pepper to taste and serve immediately, garnished with grated orange peel, if desired.