In a large, deep skillet, heat the butter over medium high heat until foaming. Add the olives and cook, stirring, until sizzling, about 2 minutes. Add the tomato sauce and bring to a simmer. Remove from the heat and set aside. Bring the salted water to a boil in a large pot over high heat. Cook and drain the gnocchi. Bring the tomato sauce back to a simmer over low heat. Add the gnocchi and stir gently with a wooden spoon until coated. Stir in the grated cheese and basil. Check the seasoning, transfer the gnocchi to a platter, and serve immediately.