IN THE BIRTHPLACE of sushi, a pizza obsession has been developing.

Pizzerias specializing in artisanal Neapolitan-style pies have popped up at a brisk pace across Japan, with chefs tackling the craft of pizza with the same meticulous zeal that has made the country a culinary star in other cuisines. (Nearly 50 French restaurants in Tokyo have at least one Michelin star.)

The...