“We want people to feel lucky to be there, like it’s Augusta,” Mr. Gehani said, referring to the home of the Masters golf tournament.

What separates car country clubs from racetracks is the amenities. They’re not just for the wealthy gearheads who want to talk about their cars. They’re for their spouses and children, as much to make the experience more luxurious as to provide car enthusiasts with a way to step away and race for a bit.

In addition to the track, the Concours Club has a 7,000-square-foot clubhouse, where the restaurant will be operated by a popular Miami chef, Brad Kilgore. The infield of the track has a football-field-size shade structure for people who want to dine with the roar of racing. There’s an 11,000-square-foot garage to service the racecars and, of course, clean and detail them.

Other tracks helped inspire the Miami club. The Thermal Club, outside Palm Springs, Calif., has four tracks over 450 acres, two restaurants and a BMW performance driving school. The club has 48 bungalows for overnight stays, as well as 268 home sites overlooking the racetracks. The initiation is $85,000, with monthly dues of $1,200.

The Atlanta Motorsports Park has two racetracks and a third track for kart racing. It also has a resort pool, conference center, outdoor cooking facilities and a putting green.

As at Concours, memberships are tiered. An initial group of 10 founding members paid $200,000 to join. The top membership now costs $50,000 for 180 days of track time and runs down to $10,000 for 60 days. A karting membership costs $2,500. (Monthly fees range from $150 to $225 a person, plus a daily fee of $30.)

The granddaddy of these clubs, Autobahn Country Club in Joliet, Ill., began as one man’s desire to recreate the golf clubs of his youth, just for cars.