Add the olive oil and butter to a large sauté pan, and place over medium heat. When the butter is melted and the oil is hot, add the shallots, garlic, salt and black pepper. Cook till the shallots and garlic are soft (do not brown the garlic).
Add the wine, broth, lemon juice, zest, and dried basil. Bring to a boil for 2-3 minutes.
Add the Maine shrimp meat. Allow to cook for 1-2 minutes, watching carefully so as to not overcook the shrimp. As soon as the shrimp lose their transparency they are done.
Pour the mixture over the cooked linguini, toss to mix well.