WASHINGTON—Justice Neil Gorsuch survived a Senate grilling to get his seat on the Supreme Court. Now, as the court’s most-junior member, he’s the chief justice of the grill.

Tradition dictates that each newcomer to the nation’s highest tribunal must serve on the committee that oversees the court’s cafeteria, a 185-seat facility open to the public on the building’s ground floor.

It isn’t a job that justices relish.

“There’s not much one can do to make the fare better,” says Justice Ruth Bader Ginsburg. The committee is “a truly disheartening assignment.”

Justice Gorsuch arrives at the cafeteria as something of a stealth candidate. President Donald Trump, despite running several restaurants in his hotel empire, selected a judge with practically no food-service experience.