2. Gently place the pork in the hot oil and sear all sides until nicely browned. Meanwhile in a large bowl or large measuring cup combine the coke, the orange juice, the salsa, the cayenne, and the brown sugar and add it to a large slow cooker set to high.
3. Remove the browned pork to the slow cooker containing the cooking liquid, cover and cook until the pork is literally falling apart when poked with a fork, about 2-3 hours.
4. Remove the meat to a clean work surface and, when it is cool enough to handled, shred it in a similar fashion to the way you would for pulled pork.
5. Remove the liquid to a large sauce pan over high heat, stir in the lime juice and bring to a boil. When the sauce comes to a boil stir in the thickening slurry and continue stirring until the sauce thickens. Correct seasoning with salt, black pepper, and cayenne.
6. Remove the pan from the stove and transfer 3/4 of the thickened sauce to a serving dish, lower the heat to low and return the sauce pan containing the remaining 1/4 of the sauce to the heat, add the meat and stir to thoroughly coat the meat. Turn off the burner under the pan.
constructing and frying the burritos:
1. Working with one tortilla shell at a time, place a tortilla shell in front of you, spread about 3 or 4 tablespoons of the carnitas evenly over the surface of the shell and, beginning at side closest to you, tightly roll the shell (jelly roll style) away from you until it is fully rolled up, push one toothpick through the roll pinning the loose end in place. Continue until all the shells and carnitas are used up.
2. Heat about 1/2-inch of vegetable oil in a frying pan over medium heat until the ripple stage.
3. Add 1 or 2 of the burritos to the hot oil and fry for about a minute on each side until each burrito is golden and crispy. Remove the fried burritos to a paper towel lined dish to absorb excess oil.