WILDLIFE SIGHTINGS MAY NOT BE GUARANTEED, but we spot our first game just hours after arriving in Namibia. As we make our final approach to Wolwedans, Dave Bradbrook, the 32-year-old pilot at the controls of our plane, begins to mutter: Five hundred feet away, loitering squarely in the middle of the runway, stands the country's national animal, a 400-pound, painted-face antelope called the oryx. We're tracking a path to flatten our first attraction.

Three hundred feet later, our wheels touch down. The oryx doesn't budge.

Part of a safari's appeal is living out the dream of affluence and ease in the bush: relaxing with a book in the oak-and-leather hunting room, sipping a rock shandy under the lazy twirl of a ceiling fan, lolling carefree about the expansive property.

One hundred feet, and Mr. Oryx stares at us with bovine nonchalance—this is one impassive antelope. Dave begins cursing. Finally, just before the propeller slice-and-dice, the oryx springs out of the way. Dave breathes and slumps back in his seat.

We've landed on the NamibRand Nature Reserve. Like so many private parks and ranches springing up around Africa, the reserve, on the eastern boundary of Namib Naukluft Park, effectively expands the amount of protected land by creating a 695-square-mile buffer zone for the adjacent park while simultaneously capitalizing on the stream of visitors it generates. At the heart of the NamibRand sits Wolwedans, a collection of three small luxury lodges balanced on shifting red desert sands.

Part of a safari's appeal is living out the expatriate dream of affluence and ease: relaxing with a book in the oak-and-leather hunting room, sipping a rock shandy under the lazy twirl of a ceiling fan, lolling carefree about the expansive property. Wolwedans specializes in this opulence. The simple eucalyptus-and-canvas chalets and lodge emanate colonial elegance, with tables set in crisp white linens and silver, rich mahogany furniture, and flaxen light cast by oil lanterns. The cuisine is decidedly Old World as well—one night we eat pumpkin mousse in puff pastry, beef consommé with wild boar ravioli, and pan-fried zucchini served over an oryx steak. (It seems not all oryx get off the runway fast enough. In fact, Bruckner later tells me that game, including antelope, zebra, and even crocodile, is farmed widely throughout the country, just as cows are raised for meat in the United States.)

Easing into the reverie is a decidedly sluggish program: breakfast on the deck, a morning drive in the park, an afternoon nap by the pool, another Land Rover tour when the heat recedes, and finally a four-course wine-and-game extravaganza that stretches into the night. With the exception of small herds of oryx, zebra, and springbok, a sleek brown-and-white miniature antelope, we don't see much game on our drives. But who cares when each evening's tour wraps up with a dune-top repose, accompanied by nosh and Sapphire-and-tonic sundowners.

Our last night in the Namib Desert, Jen and I dine with Bruckner, who tells us about a remote lodge he's building on the far side of the reserve. When the main course is served—a springbok steak in a balsamic reduction—the trip's purpose rushes into focus. I might not be able to expand my life list of animal sightings, but I'm doing a pretty good job polishing off a menu's worth of them. As Bruckner explains game management and Jen knifes into her steak, I quietly christen the trip a culinary safari. After all, I'm less likely to spot the Big Five than to eat my way through a delectable five of oryx, springbok, ostrich, kudu, and zebra. Two down, three to go.