Cream the soft butter in a small bowl by beating it against the sides of the bowl with a wooden spoon until soft and fluffy. Beat the eggs and egg yolks with a fork or whisk in another small bowl until they are well-blended, then stir in 2 oz. grated cheese. Put both bowls aside.
Heat a large fireproof serving bowl or an earthenware dish in a 200 F oven. At the same time, bring the water and salt to a bubbling boil in a large saucepan. Drop the spaghetti over high heat, stirring occasionally, for 7 to 12 minutes until it is tender. Meanwhile, fry the pieces of bacon in a fairly wide frying pan over a moderate heat until they are crisp. Pour off about half the bacon fat and stir into hte pan and the optional red pepper and then the cream. Bring the cream to simmering point and keep it warm until the spaghetti is done.
When the spaghetti si cooked, drain it thoroughly in a large colander, lifting the strands with two forks to make certain all the water runs off. Transfer the spaghetti to the heated serving bowl and stir inthe creamed butter, tossing and turning the spaghetti with two forks to coat every strand. Then stir in the hot bacon and cream mixture and finally the beaten eggs and cheese, mixing everything together thoroughly. The heat of hte pasta and other ingredients should cook the raw eggs on contact. Taste an dseason with salt and pepper. Serve the carbonara at once, the rest of the grated cheese being handed round at the table.