Cook the spaghetti in a large pot of lightly salted, boiling water until tender, about 8 minutes. While the pasta cooks, place the oil and butter in a large skillet set over medium heat. When the butter is melted, add the chilies and garlic and cook until fragrant and the garlic lightly golden, about 1 minute. Add the stock and bring to a simmer. When the spaghetti is cooked, drain well and reserve 1/2 cup of its cooking liquid. Add the spaghetti, reserved cooking liquid, basil, cheese and salt to the skillet. Toss to combine and serve.