Heat the extra-virgin olive oil with the butter over medium-low heat in a skillet with high sides. Add garlic and shallots and season with salt and pepper then cook gently until caramelized about 20 minutes, stirring occasionally.
Meanwhile heat a large pot of water to boil for pasta, salt the water very liberally then add spaghetti and bring to a rolling boil. Cook to al dente. Add 2 ladles of starchy cooking water, about 1 cup, to the shallots and stir. Drain pasta and add to shallots. Add the parsley and cheese and more black pepper, to taste. Toss 1 to 2 minutes for liquid to absorb and serve. WOW! Talk about yum-o!