Preheat the oven to 375 degrees F. Line a baking sheet with foil and coat with cooking spray.
Place the barramundi fillets on the prepared baking sheet, rub with 1 teaspoon olive oil and season with ¼ teaspoon and ¼ teaspoon pepper.
Bake until the fish is just cooked through, 10 to 12 minutes.
Heat 1 teaspoon olive oil in a large nonstick skillet set over medium heat. Cook the mushrooms until they release and then reabsorb their juices, about 5 minutes. Transfer the mushrooms to a bowl.
Heat 1 teaspoons olive oil in the skillet. Add the shallots and garlic, and cook until the shallots are starting to soften, about 2 minutes.
Add the remaining teaspoon of olive oil, then stir in the flour and cook, stirring, for 1 minute. Pour in the chicken broth and Marsala wine and simmer, stirring frequently, until the sauce is slightly thickened, about 2 minutes. Season with the remaining ¼ teaspoon of salt and pepper.
Add the cooked fish and mushrooms to the skillet and cook until the fish is heated, about 2 minutes.