Preheat the broiler and position a rack 6 inches from the heat. Line a rimmed baking sheet with foil. Arrange the fillets on the prepared baking sheet.
In a small bowl, mix the Parmesan with the mayonnaise, lemon juice, basil, oregano, and onion powder. Season with salt and pepper.
Spread the mixture on the fish and transfer the baking sheet to the oven. Broil for 3 minutes, or until the top is browned and bubbling.
Reduce the heat to 300°F and continue to roast the fish for 3 to 5 minutes, until just cooked through.
In a large, nonstick skillet, melt the butter with the olive oil. Cook the zucchini, stirring occasionally, until beginning to soften, 2 to 3 minutes. Season with salt and pepper.
Transfer to plates and top with the fish. Garnish with more Parmesan and serve.
