1 lbs. (500gr.) Spaghetti or Penne (not a thin pasta, i.e. Cappellini)
3.5 oz. Pecorino Romano (Roman Cheese from sheep’s milk, (sharp cheese)
1 cup of pasta water
3 tbls. salt for the pasta water
2 tbls black pepper (freshly ground)

for Pasta Alla Gricia additionally:

3.5 oz guanciale (jowl bacon, but pancetta or regular bacon will do)
1 pinch red hot pepper
1 tps. olive oil

Grate the cheese (or have it ground at the deli counter). 

Put on a pot of water for the pasta and salt.  When the water comes to a roiling boil add the pasta to the pot. Look at the package to see the cooking time, but it is normally between 8 and 10 minuets. 

1 minuet before the pasta is finished take out 1 cup of pasta water

Drain pasta, and place in a large bow. 

Add ½  cup of pasta water and quickly toss.

Throw the Cheese on top with the pepper. Toss quickly

Add additional pasta water to taste.

For Pasta All Gricia

Fry the bacon in olive oil and a pinch of hot pepper to taste, while you are waiting for the water to boil. 

The bacon should be done so that it is not too crispy. 

Toss in fried bacon into the pasta with the cheese