“Sometimes things weren’t done the way we wanted, but nothing was unresolvable,” Mr. Carter said.

Recently, political turmoil following the 2017 Catalan bid for independence has discouraged some foreigners from buying property in this region.

While more international investors than ever bought Spanish real estate in the first half of 2018, in Catalonia the number fell by 5.3 percent.

But building a luxury home at PGA Catalunya Resort is still a draw for overseas investors. Sales are up 9 percent from last year. Potential buyers can expect to spend around half a million euros for the land and an additional €1 million to €3 million for a house that complies with the club’s strict architectural guidelines.

A few holes down the course from the Carters’ villa, beside the lake on the 15th hole, a crane looms over the building site where Sarah and Oliver Kesting’s new home will soon stand.

The Kestings, who until recently led a hectic life juggling the management of their electronics company with school runs into traffic-congested downtown Munich, have enrolled their children in a local school and hope to move here permanently.

While construction is underway, they are staying nearby and keeping a close eye on developments.

On a recent afternoon, they climbed a paint-splashed ladder onto what will be the first floor of their new home. Black rubber tubes dangled from concrete slabs, and a microwave sat in a pile of rubble, a long cable connecting it to the mains so that the workmen could heat up their lunches.