Rising sharply from the topaz surface of the Tyrrhenian Sea, the Italian island of Ponza has never lost its primeval aura. Though its port towns today have tight clusters of confetti-colored houses, Ponza’s beaches are backed by embankments of raw lava petrified into striking shapes—a natural monument to the earth in its formative years, and a reminder of how this outpost looked to the Etruscans and Greeks who arrived here on early explorations of the area. 

“We’re out here in the middle of the sea, following in the footsteps of Ulysses and reconnecting with the philosophy of the ancient Greeks,” says eminent Roman artist (and protégé of Cy Twombly’s) Alberto Di Fabio, who purchased a remote property on Ponza a decade ago, transforming the white stucco home over long summers into...