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Step 1
Heat oil in a large pot or dutch oven over medium high heat. Mix 2 tsp salt, 2 tsp pepper, ½ Tbsp oregano and ½ Tbsp cumin, then rub all over pork chunks. Add pork to the heated pot, working in batches if necessary, and sear on all sides.
Step 2
Juice lime and oranges into a bowl, reserving the juiced citrus pieces. Mix thyme and remaining salt, pepper, oregano and cumin into the juice.
Step 3
Place sliced onion in a slow cooker, then top with pork chunks. Add on top reserved citrus pieces, along with garlic and bay leaves. Pour Coca-Cola all over the pork, followed by the juice mixture. (Do not pour the Coke after the juices, as it will rinse the seasonings off of the pork)
Step 4
Cover and cook on low for 8 hours, or on high for 4-5 hours, until pork is easily shreddable with a fork.
Step 5
Remove pork chunks to a oiled baking sheet. Broil on high for about 5 minutes, until it is browned and crisp.
Step 6
Using two forks, shred the pork.
Step 7
Serve in tacos or burritos, with rice and beans, or on nachos.