In a high-sided skillet over medium heat, add the canola oil. When it is hot toss in half the onion (reserve other half for the online Round 2 Recipe Grilled Chicken and Apple Wraps) and cook until softened, about 5 minutes. (Reserve 4 pieces each of squash, and zucchini for the online Round 2 Recipe Grilled Chicken and Apple Wraps.) Add the remaining squash and zucchini, mushrooms, and broth and season with salt and pepper. Place the fish on the vegetables and top each piece with a sprig of thyme. Season the fish with salt and pepper, cover, and steam until the fish is cooked through, about 10 minutes.
Remove the fish to a plate and cover to keep warm. Remove the vegetables with a slotted spoon to a bowl and cover to keep warm. Turn the heat to high and let the broth bubble, add the garlic and mustard and let cook until the sauce reduces and thickens, 3 to 5 minutes. Taste and add more salt and pepper, if needed.
Spoon the vegetables onto a plate and top with a piece of fish. Pour the sauce over the fish and serve.