Heat large saucepan over medium heat. Add 1 tbs oil and swirl to coat bottom. When oil is hot, add the shrimp and saute, stirring, until shrimp are pink, about 1 minute. season with salt and pepper. Transfer the shrimp to a plate and set aside.
Add the remaning tbs of oil and 1 tbs of butter to the pan. When the mixture is hot, add the garlic and onions and saute until soft, 1 to 2 minutes. Add the rice and saute until rice is opaque, about 2 minutes. Add the wine, deglaze the pan, and simmer until liquid is absorbed by the rice, 2 to 3 minutes.
Ladle in the stock 1/2 cup at a time, allowing each addition to be absorbed by the rice before adding the next. Continue until the rice is al dente, about 10 minutes. Return the shrimp to the rice, add the basil,the remaining 2 tbs of butter and the lime juice, and stir. Taste and adjust the salt and pepper if needed.