In a large skillet, heat the olive oil until shimmering. Add the lemons and cook over medium-high heat until most of the moisture has cooked off—about 5 minutes.

Stir in the sugar and reduce the heat to medium-low. Cook for another 3-4 minutes, until the lemons are caramelized.

Add the shallot and garlic. Cook until softened—about 3-4 minutes. Turn off the heat until the pasta is ready.

Bring about 2 quarts of generously salted water to a boil. Cook the pasta 1-2 minutes shorter than the indicated time on the package.

Use tongs to transfer the pasta to the skillet along with 1 cup of the cooking liquid. Bring to a boil and cook until al dente, adding more pasta water if needed.

Stir in the Parmesan, parsley and lots of freshly ground black pepper. Taste for salt and add more if needed. Serve with toasted breadcrumbs if desired.