Place pork shoulder in your slow cooker with the garlic, cumin, salt, black pepper, and cayenne pepper, and cook on low for 6-7 hours.
At this point, smash the cooked garlic cloves to blend them into the juices that have been released by the pork.
Peel and slice the onions and add them to the slow cooker, along with the juice of 1 lime. I like to add the onions when there is only an hour or two left in the cooking process so that they don't burn or become so well cooked that they lose all consistency. With an hour or two cooking time they caramelize perfectly without disappearing. That said, if you will be away from home, you can add all ingredients together at once from the beginning.
After 8 hours, the pork should be tender. You can now remove it from the slow cooker and serve it as is, or proceed to make a crispier carnita by frying them in a cast iron skillet in some lard (our new favorite way of doing it).
Heat a cast iron skillet to high heat and melt in some lard while you are lightly shredding the cooked pork.
Brown the shredded pork in the lard. If you like it really crispy, you can use high heat, and flip the carnitas to brown the other side too. Just try not to cook them for too long so that the meat doesn't dry out.
Serve with the caramelized onions on homemade tortillas with the toppings of your choice.