ABOARD THE ATWOOD ADVANTAGE — In the ship’s control room, facing four video screens, a driller from Mississippi in dark shades and a black baseball cap with a skull on it held what could be the future of Israel in his hands.

The massive drill he controlled extended down 11,345 feet, more than two miles below the surface of a calm Mediterranean Sea, as it plunged deeper and deeper into one of the biggest natural gas fields discovered in the world in recent years.

Once a barren energy island in a part of the planet otherwise awash in resources, Israel is, after years of delay, finally pushing ahead with an ambitious strategy to tap offshore reserves that could transform its economy and, it hopes, its place in a historically hostile region.

If all goes according to plan, Israel will not only become largely energy-independent, it will also supply neighbors that will have new reason to be friends.