Andrea Rodriguez, AP

The 3.5 million tourists who flooded Cuba last year downed oceans of mojitos, lakes of daiquiris and rivers of thin, sour beer. Only an odd few accompanied their ropa vieja and croquetas with wine — mostly overpriced, low- to mid-grade vintages from Chile, Argentina and Spain.

That may be about to change, at least around the margins of Cuba's once-dismal dining scene. Some of the United States' largest vintners want to turn this island of sweet rum and flat state-brewed beer into a haven for robust California zinfandel, oaky chardonnay and powerful cabernet sauvignon.

Thousands of private restaurants have cropped up around Cuba in recent years under economic reforms designed to soften the shock of cutbacks in the troubled state-controlled economy. Particularly on the high end, those restaurants' clients are increasingly American, part of a 76 percent surge in U.S. tourism — to 161,174 last year — that followed Presidents Raul Castro and Barack Obama's declaration of detente at the end of 2014...