Cut pork pieces crosswise into thirds. Cut off any big chunks of fat from pork and reserve; leave small pieces of fat attached to pork. Combine pork, reserved fat, 2 cups water, and next 4 ingredients in deep 12-inch skillet. Bring to boil. Reduce heat, cover, and simmer until pork is tender, stirring occasionally, about 1 hour 45 minutes, adding more water by 1/4 cupfuls if necessary to keep pork partially submerged.
Uncover; boil pork mixture until liquid is reduced by half, about 10 minutes. Stir in brandy; boil until liquid evaporates and meat browns and begins to get crisp, stirring often, about 15 minutes. Cool meat slightly. Discard any loose pieces of fat. Tear meat into strips; return to skillet. (Can be made 1 day ahead. Cover and chill.)
Add 2 tablespoons water to skillet. Cover and rewarm pork over medium-low heat, stirring, about 5 minutes. Season with more salt, if desired. Transfer to bowl. Serve with warm tortillas, Avocado Salsa, and tomato salsa.
