ZAGAROLO, Italy—On a recent Sunday, Claudia Proietti whipped up a sumptuous lunch of cheese and black pepper ravioli in an asparagus and guanciale sauce, slow-cooked veal and roast potatoes.

The 60-year-old picked the herbs from the garden behind her rustic home in this town just outside Rome, while the olive oil and white Malvasia wine came from the small farm she and her husband own. The smell of baking bread filled the living room, where she would serve lunch, topped off with a rosemary Bavarian cake and ice-cold limoncello.

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