Place the water in a large sauce pan over high heat.
Place a large skillet over high heat. Spray lightly with olive oil. Add the sliced mushrooms and cook, stirring frequently, until the mushrooms are lightly browned. Remove to a plate and set aside.
When the water boils, add the linguine.
Place the olive oil in the pan used for the mushrooms, over medium-high heat. When the oil is hot, add the garlic and shallots and sauté, stirring frequently. Do not allow the garlic or shallots to brown.
When the linguine is almost done, add the lemon zest, shrimp and mushrooms to the skillet with the shallots and garlic. Cook, tossing frequently, until the shrimp begin to turn pink.
Add the lemon juice. Toss and add the milk and the Parmigiano-Reggiano. Toss, then add the pepper and basil.
Add the cooked linguine to the shrimp mixture and toss until well coated. Add about 1/4 cup of the pasta water. Cook over medium heat for about 1 minute, tossing the ingredients together well. When the sauce is slightly thickened, serve.
