Preheat the oven to 300 F degrees.
Cut the pork shoulder into 3- to 4-inch chunks, trimming and discarding as much of the excess fat as possible. This cut is extremely well marbled so don't attempt to remove all of the fat, just trim the excess around the edges of each chunk the best you can. Transfer the pieces of pork to a large Dutch oven. (You'll end up tossing some pieces that are mostly fat. This is why you want to start with a 4+ pound roast).
Combine the Carnitas Seasoning Mix ingredients in a small bowl and sprinkle over the pork. Toss lightly to distribute the seasoning. Add the quartered onion, garlic, the juice from the oranges and limes, the spent orange halves only (discard the spent lime halves), and the bay leaves.
Cover the pot, transfer to the oven, and cook for 2 ½ to 3 hours or until the meat is very tender and easy to shred. Remove the pot from the oven.
Coat a large rimmed baking sheet with nonstick cooking spray. Use a slotted spoon to transfer the chunks of pork to the baking sheet and using two forks, shred the meat into small pieces. Measure out ½ cup of the juices from the Dutch oven and pour it over the shredded pork, tossing to combine. Spread the pork out in an even layer.
Set your oven to BROIL. Transfer the baking sheet to the oven and broil for about 3 minutes, until browned and crisped. Remove from oven and use a spatula or tongs to toss the carnitas, then spread back out in an even layer. Return the baking sheet to the oven for an additional 2 to 3 minutes, or until crisped to your liking. Watch closely so it doesn't burn.