When Sonoko Sakai’s mother snuck a little miso into her lasagna, she wasn’t thinking of the kind of Japanese fusion that became an American dining craze in the 1980s.

Rather, she was doing what Japanese cooks had been doing for centuries: adapting to outside influences. Many dishes now thought of as quintessentially Japanese are fusions once considered foreign to the country.

Gyoza dumplings arrived from China only about a hundred years ago. Tonkatsu, a fried pork cutlet, came from French chefs cooking in the imperial court after Japan opened to the West during the Meiji period of the late 1800s.

Each dish was adapted to be more, well, Japanese, said Sakai, a Japanese American cooking instructor who explores this combination of influences in her new book, “Wafu Cooking.”

Wafu literally means “Japanese in style.” That could mean blending Western and Japanese flavors or even adjusting a dish’s presentation or sensibility to Japanese tastes.

Sakai routinely wafues Western dishes — she is pushing the use of wafu as a verb — such as a white-bean chili in her book made extra savory from soy sauce.

“I find that it enhances the flavor,” Sakai said. “It doesn’t make it alien or foreign. You just wonder why it tastes better.”

Slipping in an ingredient on the sly is also a Japanese tradition, one called kakushiaji. It means “secret flavor,” but Japanese cooks think of them more like secret agents, Sakai said.

She sneaks sake, soy sauce and ginger into her Italian wedding soup, a dish she learned from relatives on her grandmother’s side, who are from the Italian part of Switzerland. The pork meatballs are similar to the filling she makes for her gyoza, using potato starch as a binding agent instead of the egg in Italian meatballs.

“I didn’t have to reinvent this recipe,” Sakai said. “I’m just doing what I do.”