Bring a large pot of water to a boil, cook pasta according to package directions.
Meanwhile, in a skillet sauté garlic with olive oil and just before it turns golden add Brussels sprouts and sauté over high heat for 2-3 minutes. Add wine and reduce quickly, season with salt and pepper.
Drain pasta, reserving ½ cup of pasta cooking water.
Add pasta cooking water to Brussels sprout mixture; toss mixture over high heat.
Remove from the heat. Toss with cheese and top with basil.
