Place a heavy bottomed skillet (cast iron preferred) with one or two tablespoons of coconut oil to heat over medium high heat.
When the pan is hot enough, add the sliced onions and cook, stirring occasionally, until they become soft and golden, about 10 minutes. Add a few tablespoons of water as necessary when the onions start attaching to the pan a little too much.
While the onions are cooking, rinse the chicken livers under cold running water. Drain well, pat dry and remove white connective tissue, if any. Set aside.
When the onions have taken a nice golden coloration, add the salt pepper, nutmeg and apple. Continue cooking for 4-5 minutes, until the apple becomes soft and tender. Again, add a little bit of water as necessary if you find the mixture attaches too much.
Add the chicken liver (just make sure that the liquid is completely evaporated before you add the liver). Continue cooking for an additional 5 minutes or so, until the liver is brown on the outside but still slightly pink on the inside. Kill the heat, cover and let stand for about 5 minutes.
Transfer the mixture to the bowl of your food processor and give that a few spins on pulse, just to break everything down.
Start the motor again and this time, while the blade is turning, drizzle in the melted coconut oil, followed by the coconut milk. Let that spin for an extra 30 seconds, then strain the mixture through a fine mesh sieve. You might want to help it through by swirling it around with a ladle (while this step is entirely optional, it is what will make your pâté extra creamy and velvety smooth, so I think it's really worth it. Don’t worry too much about wasting some of your precious concoction in the process: only a few tablespoons end up being left behind, and you can always munch on that, or give it to your furry friends as a nutritious treat!)
Pour the mixture into 6 individual half cup ramekins and place in the refrigerator to set for at least 4-6 hours.
Cover loosely with a plastic wrap if keeping for an extended period of time, to prevent the top from drying out.
This pâté will keep for about 3-4 days in the refrigerator and it also freezes very well. Just take it out of the fridge the night before and it’ll be good to go by morning.