Place the head (frozen or fresh) in a large stockpot (like a seriously, seriously large pot). Fill the container with filtered water.
Bring the pig head slowly to a low simmer. Cover and leave the pig head to simmer for 24 hours on low heat. By the time the head is finished, it will be in pieces.
Remove the head from the stockpot with care and place it on a large platter (reserve the cooking liquid). Allow it to cool before separating the meat from the bones with your hands.
Put the meat in a large mixing bowl. Season with sea salt and pepper to taste. Because headcheese is typically eaten at room temperature, err on the side of extra salty.
Return the cooking liquid to a simmer. Continue to simmer the stock vigorously until the liquid has mostly reduced and is slightly thickened.
Put the shredded meat in a pan (like a loaf pan). Pour the reduced liquid over the meat until it is completely submerged in the pan.
Refrigerate the headcheese until firm. The liquid will set, resulting in a gelatinous loaf of... meat.
Serve the headcheese cold with a crusty loaf of bread. (Or whatever you want!)
Eat the loaf within a week or freeze it for later use.