Step 1Cook the linguine in a large pot of rapidly boiling water until al dente, about 10 minutes. Drain and set aside. Place the dried mushrooms and water in a small bowl to soak. Set aside.
Step 2Meanwhile, heat 1 tablespoon of oil in a 12-inch nonstick skillet over medium-high heat. Add the garlic and onion. Cook until heated through and fragrant, about 2 minutes, stirring often. Add the fresh mushrooms, oregano and 1/2 teaspoon of salt. Add the dried mushrooms and liquid. If the liquid is gritty, strain through a filter paper or triple thickness of cheesecloth placed in a small strainer. Cook, uncovered, until the mushrooms have cooked through completely and the mixture has thickened, about 5 more minutes, stirring often.
Step 3Stir 2 tablespoons of the flour into 1/4 cup of the chicken broth. Add to the skillet along with the remaining broth and wine. Simmer, uncovered, until the liquid has reduced by 1/3, about 7 minutes. Remove from the heat. Stir in the linguine and 1/3 cup of the cheese. Transfer to a greased 10-cup-capacity shallow baking dish. Wash and dry the skillet.
Step 4Cut the chicken into 1-inch dice. Combine the remaining 2 tablespoons of flour, the remaining 1/2 teaspoon of salt and pepper to taste in a large plastic food bag. Add the diced chicken in batches. Separate the pieces if stuck together. Shake to coat the chicken. Set aside.
Step 5Heat the oven to 350 degrees.
Step 6Heat the remaining oil in a skillet over high heat. Add the chicken. Stir-fry until light-brown on all sides, about 5 minutes. Stir into the linguine mixture. Adjust the seasonings to taste. (This can be made 2 days ahead and refrigerated, covered with foil. Let stand at room temperature 1 hour before baking if chilled.)
Step 7Stir in the basil leaves. Lightly compress the ingredients to flatten the surface. Sprinkle the remaining cheese over. Bake the casserole until browned, about 45 to 50 minutes. Serve hot. Spoon some of the liquid in the bottom of the dish over each serving.