Set up two pots: one for boiling the pasta and another for mixing the pasta with the lemon and butter.
Bring water to a boil in the first pot and add a generous amount of salt.
Add the spaghetti to the boiling water and cook for no more than 9 minutes.
While the pasta is cooking, place the empty pot on top of the pasta water to warm it with steam.
Do the same with the pasta bowls to ensure they are warm, as serving the spaghetti on a cold plate is a mistake.
Once the pasta is al dente, turn off the burner and keep the spaghetti in the pot with the water.
Ladle a couple of cups of boiling pasta water into the empty pot to keep it warm, then discard the water.
Add another ladle of fresh pasta water into the empty pot to start your sauce.
Squeeze the juice from two halved lemons into the pot, using a strainer to catch the seeds.
Using tongs, remove the spaghetti from the pot and place it into the pot with the lemon water.
Add butter to the spaghetti and stir it in circles with a wooden spoon to coat it with the lemon butter sauce.
During this process, the lemon, water, and butter will emulsify, with the spaghetti acting like a whisk.
Add the squeezed lemon halves to the spaghetti to infuse the zest.
Plate the spaghetti using tongs, pour a bit more lemon butter sauce on top, and generously sprinkle with Parmigiano Reggiano.
Garnish with the squeezed lemon half on the side.