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Boil the pig's head with 2 stalks celery, 1 carrot, 6 cloves minced garlic, 1 tablespoon salt, 2 teaspoons black pepper, 1/2 teaspoon dried thyme for 5 hours. Turn off heat allow to cool until you're able to handle the head. Remove the head from the pot with a meat hook, or use a dough hook from your stand mixer to help secure a grip on it. Remove the meat from the head, then place the skull back in the pot and boil for another 5 hours.
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After boiling the skull, remove it and then remove any large pieces/vegetables with tongs or a mesh ladle. The skull/vegetable bits can be discarded. Strain the rest of the liquid through a single sheet of cheesecloth and discard any particles that are stuck to the cheesecloth. Allow the strained liquid to cool to room temperature, then cover it and place it in the refrigerator overnight.
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Cut/shred the meat into roughly 1-inch bits and place in a large casserole pan or bowl. Cover and refrigerate overnight.
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The next morning, remove the liquid from the refrigerator and remove and discard the layer of fat that has collected on top (I did this using a large flat spoon).
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Take 8 cups of the liquid and bring to a simmer. Add the chopped carrots, apple cider vinegar, salt, black pepper, and thyme. Simmer for 15 minutes. Then stir in the lemon juice and rosemary. Taste, add more salt if needed. It should taste a bit tangy and just slightly too salty. Add more seasonings if needed, then remove from heat and set aside to cool.
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Now take the meat chunks out of the refrigerator and break them apart with your hands while juice is cooling. Then line a 9 x 13 inch casserole dish with plastic wrap, or (3) 4 x 12 inch loaf pans and add the meat pieces.
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Pour over meat mixture, stir, and tap the loaf pan on a flat surface several time with force to help the liquid settle all the way through. Use the flattened palms of your hands to press down really hard on the meat and mixed veggies so that they're nice and compacted. If you now have extra space at the top of the loaf pan that's just liquid, add some more meat chunks and press down again. Lay another sheet of plastic wrap over the top, and then lay down 2 bags bag of dried beans or rice over the top to help apply pressure evenly on top of the loaf. Refrigerate overnight. Done!