Little Rock’s Moody Brews, a small craft brewery in the Pettaway neighborhood, will start slinging “The Beef,” a beef dip sandwich crafted with local wagyu from Greenbrier’s Sweetwater Cattle Company.

Since the sandwich was seemingly popularized by the fourth Earl of Sandwich in late 18th century England, it has become a staple in the American diet. The average person eats six sandwiches a week ...