Fill a large pot with about 3 quarts of water, add a tsp of salt and place over high heat and bring to a boil.
While the water is coming to a boil, use a medium bowl to beat the eggs till smooth a runny. Add the cheese and mix with a fork till well blended and creamy. Season with a generous amount of black pepper. Set aside.
In a large frying pan over medium-high heat, cook the chunks of pork meat until the meat begins to brown and the fat is rendered ( 5 to 6 minutes). Set aside.
Remove about 1 tablespoon of the rendered fat and add it to the egg mixture to begin to temper the sauce, quickly whisking again with the fork.
When the water comes to a boil, add the spaghetti and stir until all the strands are submerged. Cook according to the package instructions, stirring occasionally, until the pasta is al dente.
When the pasta is ready to your liking, lift out the unstrained pasta with tongs and quickly stir it and any pasta liquid that drips from it into the frying pan with the rendered pork. You want to stir quickly so the pasta remains hot to partially cook the eggs during the next step.
Quickly pour the egg and cheese mixture and stir vigorously to avoid curdling the eggs. If too dry, add a little pasta water till you get the consistency of the sauce you want. It should be creamy but not too runny. (If you overdo the water, you can always thicken the sauce by heating the pasta on a low fire and keep stirring until the sauce thickens to your liking).
Serve with a topping of grated cheese and ground pepper.