Bring a large pot of lightly salted water with olive oil to a boil. Add linguine pasta, and cook for 8 to 10 minutes, or until al dente; drain.
In a large skillet, melt the butter over medium heat. Stir in cream, and season with pepper. Cook 6 minutes, stirring constantly.
Stir Parmesan cheese into cream sauce, stirring until mixed. Blend in the pesto, and cook for 3 minutes, until thickened.
Stir in the shrimp, and cook until they turn pink, about 5 minutes. Stir in fresh basil and serve over the hot linguine noodles.