In Italian cooking, pasta and sauce are not separate elements combined on the plate. The pasta is finished IN the sauce — tossed together in the pan with a splash of starchy cooking water to create an emulsified coating that binds sauce to pasta. This is the single technique that most dramatically separates Italian restaurant pasta from home-cooked pasta.
Cook pasta in well-salted water (it should taste like the sea). Pull pasta 1-2 minutes before al dente. Reserve at least a cup of starchy cooking water before draining. Add pasta directly to the sauce in its pan. Toss vigorously over heat, adding splashes of pasta water. The starch in the water emulsifies with the fat in the sauce, creating a glossy coating that clings to every strand. For cacio e pepe and carbonara, the pasta water IS the sauce — its starch content is the binding agent.
For cacio e pepe: use a 10-inch pan with a cup of pasta water, reduce slightly. Off heat, add the drained pasta and the cheese-pepper mixture, tossing aggressively. The temperature must be below 70°C or the cheese clumps — the pasta water's residual heat provides just enough. For carbonara: same principle, the egg mixture is tempered by the pasta's heat, not the pan's heat. Pan goes OFF the burner before the eggs go in.
Draining pasta completely and adding to a plate then ladling sauce on top. Not salting the cooking water. Rinsing pasta — you're washing off the starch that binds the sauce. Not reserving pasta water. Cooking pasta to fully done before adding to sauce — it continues cooking in the pan. Using too much water — a smaller pot produces starchier water, which emulsifies better.