Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once the water is boiling, stir in the linguine, and return to a boil. Cook the pasta uncovered, stirring occasionally, until the pasta has cooked through, but is still firm to the bite, about 11 minutes. Drain well in a colander set in the sink. Transfer the linguine to a large mixing bowl.
Heat the olive oil and butter together in large skillet over medium heat until the butter is melted. Cook and stir the garlic in the butter and oil for 2 to 3 minutes. Add shrimp and cook for 4 to 5 minutes, stirring frequently. Stir in the wine, lemon juice, red pepper, basil, and salt and cook another 1 minute. Mix in the tomatoes and cook 1 minute more; remove from heat and transfer mixture to the bowl with the linguine. Sprinkle the Pecorino Romano cheese and parsley over the pasta and sauce; toss until well mixed.
