The Mexican stewed meat dish often made with goat or beef and seasoned with dried chiles is called birria. The meat is typically marinated in an adobo of dried chiles, vinegar, garlic, herbs, and spices, then slowly cooked until tender in a richly flavored broth called consomé.
Birria is associated especially with Jalisco and western Mexico, where it historically referred to a regional style of barbacoa. Goat was traditional in many preparations, but beef became especially important in later regional versions, including the beef birria associated with Tijuana. Lamb and other meats may also be used.
Birria is commonly served with corn tortillas, onion, cilantro, and lime, either as a stew or inside tacos. Quesabirria adds melted cheese and is often dipped into consomé. Menudo and pozole are also Mexican soups or stews, but they use different principal ingredients; barbacoa is a related cooking tradition rather than the single canonical answer to this question.