Bring a large pot of salted water to a rolling boil, then cook the spaghetti for 2-3 minutes less than the time stated on the package instructions. You want the pasta to be underdone so that it can finish cooking in the sauce. Before draining the pasta, carefully reserve 1 cup of the pasta water in a liquid measuring cup.
In a large flat-sided skillet or saucepan, heat 3/4 cup of the pasta water with the butter over medium-high heat. Stir periodically to help melt and incorporate the butter.
Once the mixture reaches a simmer, turn the heat to low. Add the pasta, cheeses, and black pepper, stirring with a spatula to combine. Continue stirring for several minutes, approximately 4-5, until a sauce forms. This will take patience, and the cheese will likely clump at first since the ingredients will cool down the water. You can turn the heat up slightly, but don’t go past medium-low or you risk the cheese turning grainy. If the mixture needs thinning, add the remaining pasta water.
Divide into two portions. Top with additional black pepper if desired, and serve immediately.
When a recipe has so few ingredients, you want to use the best quality options available. If you live near a market that sells freshly made pasta, that will truly take this to the next level. But more importantly, get good quality blocks of cheese, and grate it yourself. If you can find Parmigiano-Reggiano instead of regular parmesan cheese, that’s the gold standard.