Birria (. [ˈbirja]. ) is a Mexican dish from the state of Jalisco. The dish is a spicy stew, traditionally made from goat meat or mutton, but occasionally from beef or chicken. The dish is often served as celebratory occasions, such as weddings and baptisms, and holidays, such as Christmas and Easter.n Mexican culture [edit]. Restaurants or street carts that serve birria are known as birrierias and exist through Mexico, but especially in Jalisco and its capital, Guadalajara.