Cut pork in 4 - 5 portions, place in a ziplock bag or container and add kombucha, garlic, chillies, black pepper, cumin, and oregano. Marinate overnight in the fridge.
Heat fat at low heat in a heavy-bottomed pot. If you're using achiote (or annato seeds), add them to the fat and let infuse for a minute or two, then drain the coloured fat, discard achiote and return fat to the pot.
Crank up the heat, lift pork out of its marinade (reserve it) and brown on all sides.
Add marinade, salt and onions.
Wrap red peppercorns in cheesecloth and tie with kitchen thread or pop them in a stainless steel tea infuser, and place in the pot.
Bring to a boil, reduce heat and simmer for about 2 hours, until the pork is tender.
Remove the lid, fish the pork and peppercorn package (which you can discard) out of the pot, and crank up the heat again to reduce the sauce if you like it thicker.
Serve pork topped with sauce, with baked sweet potatoes and salad on the side.