Enjoying an Irish Breakfast Bap in Dublin. A Breakfast Bap is basically a McDonald’s Sausage McMuffin with Egg on steroids: The Breakfast Roll (or its non-identical twin the Breakfast Bap) was created through the adaptation of the full Irish breakfast for the modern, mobile generation. Basically most ingredients that constitute an Irish breakfast are forced inside a demi-baguette (roll) or soft bun (bap). The place we’re staying, Charleville Lodge, has an attached Cafe, The White Moose Cafe, that serves these up every morning for about €6.50. They’re good—dang good.