Place the pig feet, pork shoulder, garlic, black peppercorns, red pepper flakes, bay leaves, onion, herbs, vinegar, carrots, and celery in a large pot. Cover everything with cold water, making sure the pork is fully submerged.

Bring the pot to a boil, then reduce the heat to a gentle simmer. Skim off any foam that rises to the surface. Simmer uncovered for 3-4 hours, or until the pork shoulder is fork-tender and the meat around the pig feet is soft and pulling away from the bone.

Cool the Meat and Strain the Liquid

Remove the pork shoulder and pig feet with tongs or a slotted spoon and place them in a large bowl. Let them cool until safe to handle.

Strain the cooking liquid through a fine mesh strainer or cheesecloth into a clean pot. Discard the vegetables, herbs, peppercorns, and bay leaves.

Bring the strained cooking liquid to a simmer and reduce it by about half. Skim off visible fat from the surface as needed. You want about 2-3 cups of rich cooking liquid for molding the head cheese.

Pour a few tablespoons of the reduced liquid onto a small plate and chill it in the refrigerator. The liquid should set lightly firm and should not slide around the plate.

Press it gently with your finger. It should spring back a little. If it does not set, reduce the liquid a little more and test again.

If the liquid still needs help, dissolve a small amount of unflavored gelatin into the warm liquid and repeat the test before molding.

Remove the meat from the pig feet and discard the bones, tough cartilage, and any pieces you do not want in the finished head cheese.

Cut the pork shoulder into small pieces for a cleaner terrine-style slice, or chop and shred it for a more rustic texture.

Line a loaf pan or terrine mold with plastic wrap, leaving enough overhang to cover the top.

Add the pork mixture to the mold. Pour in just enough reduced cooking liquid to barely cover the meat. Fold the plastic wrap over the top and press gently so the meat settles into the liquid.

Refrigerate overnight until fully set.