Melt the lard or coconut oil in a heavy skillet set over high heat.
Add the meat in a single layer, making sure that the pieces do not touch, and cook until brown on all sides. Work in several batches if you have to so you don’t overcrowd the pan. Remove the cooked pieces of meat to a bowl to collect the juices.
Once all the meat has been cooked and set aside, lower the heat to medium, add a little more fat to the pan if necessary then throw in the onion and garlic and cook, stirring often, until the onion is fragrant and becomes translucent.
Add oregano, mustard, ground nutmeg, stir to coat then add broth and white wine vinegar.
Add meat and juices back into the pan, bring to a simmer then transfer to slow cooker and cook on low for 6 hours or high for 4 hours
Add mushrooms and an extra cup of water and continue cooking for 1 hour on high or 2 hours on low
Ladle a little bit of the cooking liquid into a measuring cup - whisk in coconut milk and ghee then return to slow cooker; add capers, mix one final time and serve.