Trim roast of all fat and cut into large chunks, about 1 by 3 inches. In a large frying pan, heat 1 tablespoon of vegetable oil over medium high heat and brown the meat. As the pieces brown, remove them and place them in a stock pot.
Place the next 9 ingredients in the stock pot. Cook on low heat, simmer with the lid on, for 2-1/2 hours. Remove the roast chunks, place on cutting board and shred the meat with two forks. Place the shredded beef back into the pot with the juice and keep warm.
In a frying pan, heat 1-1/2 inches of vegetable oil to medium high heat. Heat two flour tortillas at a time in the microwave for 35 seconds on low so they are soft enough and they won't break when folding.
Once the chimichangas are wrapped tightly in the burrito, deep fry them on both sides until golden brown. Toothpicks can be used to help keep the burrito wrap in the same shape while frying them.
Remove and set on a towel until all chimichangas are cooked. Garnish with fresh cilantro, sliced limes, and your favorite salsa.
Serves 6 to 8 people or 14 to 15 chimichangas