Scrub and thoroughly dry the unwaxed lemon, then freeze it whole until solid, at least 8 hours.

Bring a large pot of water to a boil and add the kosher salt. Cook the spaghetti until al dente according to the package. Before draining, scoop out at least 3/4 cup of the starchy cooking water.

Put the butter, finely grated Parmesan, and black pepper in a large heatproof bowl. Finely grate about one-third of the frozen lemon over the bowl, catching yellow peel and a little flesh while avoiding seeds and thick white pith. Return the remaining lemon to the freezer for another use.

Transfer the hot spaghetti to the bowl with tongs. Add 1/2 cup of the reserved pasta water and toss vigorously until the butter melts and the cheese forms a thin, silky coating. Add the remaining water a tablespoon at a time if the pasta looks dry.

Divide among four bowls and serve immediately while the sauce is glossy. Taste and add a little more grated frozen lemon only if you want a sharper citrus finish.