For the trout and steak: Preheat a gas grill to medium-high heat or a charcoal grill to even, hot coals.
Sprinkle the steaks liberally with salt and pepper and rub them with 2 tablespoons of the olive oil. Grill, turning once, until cooked to the desired doneness, about 5 minutes per side for medium. Allow the cooked steaks to rest off the heat for at least 10 minutes before serving.
Place a large skillet over medium-high heat with 1 tablespoon olive oil and 1 tablespoon butter. Add the mushrooms, garlic and shallots to the skillet and cook, stirring occasionally, until the mushrooms are tender, 5 to 6 minutes. Add the wine and cook until almost completely reduced, 2 to 3 minutes. Season the mushrooms with salt and pepper and transfer to a dish.
Wipe out the skillet that the mushrooms were cooked in and return it to medium-high heat with the remaining olive oil and butter. Sprinkle the flesh of the fish liberally with salt and pepper and divide the cooked mushrooms among them, stuffing the cavity of each fish. Working in batches as needed, carefully cook the fish fillets, turning once, until the skin is golden brown and the flesh is cooked through, about 5 minutes per side.