While water is heating, place a large skillet of medium heat and add 2 tablespoons of olive oil. Sauté garlic and shallot until soft but not brown. Add breadcrumbs and stir
Increase heat to high, add cream and cook it for one minute or two, until it starts to thicken. Stir in the basil and remove from heat. Season to taste with salt and pepper. Stir in the cheese
Add the spaghetti to the boiling water and cook until al dente, about 7 minutes. Drain thoroughly.
Toss the drained pasta onto the skillet over medium heat until noodles are coated.