Remove the rind from the guanciale, then cut it into thick slice, about 0.5 cm each. Consider 2 slices per person. Cut each slice into sticks.
Heat the pan, then with use a piece of rind to grease its surface (see video below). Add the guanciale, that will start immediately to fry (pay attention: it should become transparent, don't burn it). The right texture of the guanciale, not burnt but not even boiled, is crucial to the success of this recipe. In the meanwhile, start heating the water and salt it.
When the guanciale has released its fat and looks crispy, add the tomato sauce. With a cover (otherwise it gets too dry), cook it for about 15 minutes. Add black pepper according to taste (personally I prefer to skip this, since the guanciale rind is already rich in black pepper and some of that sticks to the fat).
When the pasta is almost ready (2 minutes in advance of cooking time) remove it from the water and drop it into the pan. With the spoon, stir it. Then, add some pasta water and go on stirring. Repeat until it is cooked. The pasta water, high in starch, will help creating a wonderful cream, when added to...
... the fat contained in the pecorino romano. This is final step: add the pecorino, stir it and your amatriciana is ready to be served. Buon appetito!