Cook linguine in large pot of boiling salted water until just tender but still firm to bite, 4 minutes. Drain, reserving 1cup pasta cooking liquid. Return pasta to same pot.
Meanwhile, heat olive oil in heavy large skillet over medium-high heat. Add 1/2 cup basil, garlic, and crushed red pepper; stir 1 minute. Add wine and boil until slightly reduced, about 3 minutes. Add mixture from skillet, remaining 1/2 cup basil, and 3/4 cup cheese, to pasta. Toss over medium heat until sauce coats pasta, adding reserved pasta liquid by 1/4 cupfuls if dry. Season with salt and pepper. Transfer to bowl. Sprinkle with remaining 3/4 cup cheese.
