Bring a large pot of water to a vigorous boil. Generously salt the water—approximately 2 tablespoons for every 500 grams of pasta. The water should have the salinity of the sea.
In a mixing bowl, beat the eggs until uniformly combined. Fold in the grated cheese and an assertive amount of freshly ground black pepper. The mixture should be thick and cohesive. Set aside.
Place the guanciale in a cold skillet and set the heat to medium. Allow the fat to render slowly, cooking until the meat is golden and crisp at the edges, about 5 to 7 minutes. Do not allow it to become overly crisp. Remove from heat, transfer the guanciale to a plate using a slotted spoon, and retain approximately 2 tablespoons of the rendered fat in the pan.
Cook the pasta in the boiling water until just al dente, following the timing on the package. Reserve ½ cup of the starchy cooking water before draining the pasta.
Add the hot, drained pasta to the pan containing the reserved pork fat. Toss to evenly coat the noodles. Take the pan completely off the heat to avoid curdling the eggs.
Gradually add the egg and cheese mixture to the pasta, stirring vigorously or tossing with tongs to form a glossy, emulsified sauce. Incorporate a small amount of the reserved pasta water as needed to loosen and bind the sauce properly.
Fold in the crisped guanciale, reserving a few pieces for garnish. Serve immediately, topped with additional Pecorino Romano and a final crack of black pepper.