In a medium bowl, combine brown sugar, ancho chile pepper, smoked paprika, coarse salt, white pepper, dried cilantro, cumin, coriander, and red pepper flakes. Mix well to combine. Rub pork shoulder with spice mixture, making sure to coat all sides.
Pour cola and water into the bowl of a slow cooker. Place seasoned pork shoulder on top. Squeeze juice from oranges and limes on top of pork, then add the remaining peels to the slow cooker as well. Add whole garlic cloves to the liquid in the pot.
Cover and cook for about 8 hours on low. Pork should be moist and pull apart easily. Check around 6 hours, then continue cooking in 30 minute increments until fully cooked.
Transfer the meat to a cutting board and pull it apart with two forks.
Place the shredded meat in a large skillet with a touch of olive oil. Cook (in batches if necessary) over medium-high heat for about 3 to 5 minutes, until edges are slightly crispy and meat is still moist. Remove from heat and transfer to a large bowl.
Chop the tomatoes, onion, and green onions. Thinly slice the avocado.
Separate the top and bottom rolls and roll flat using a rolling pin. These will be your “tortillas” for the tacos. (Alternately, if you prefer tostadas, you can lightly grill the flattened rolls and serve flat with toppings.)
Top each flattened roll “tortilla” with pork carnitas and toppings of choice. Serve with chips and salsa.
See also companion recipes:
Recipe adapted from: https://www.cravingsofalunatic.com/sweet-and-spicy-slow-cooker-carnitas.