Adding a stuffed crust to a pizza chain’s menu doesn’t seem like a big deal. But for Domino’s Pizza, it’s more than three decades in the making.

Domino's Pizza on Monday posted a surprise decline in first-quarter same-store sales in its biggest market, as elevated inflation and economic uncertainty hit consumer appetite for restaurant food.

Domino’s hesitance to add the item comes with the increase in time it takes to make a stuffed pizza: It involves an intricate process of laying out the string cheese, folding the dough to ...