Add a tablespoon of chicken fat and a tablespoon of butter to a medium heavy-bottomed pot and add your sliced onions and thyme. Cook over medium heat until onions are soft.
Add cinnamon, bay leaf, star anise, and black peppercorns to a spice grinder and pulse until finely ground (your cinnamon should already be ground, but adding it to the grinder helps the ingredients to move around and get ground up).
Add the spicing to the onions and cook over medium heat until the onions are soft and deeply caramelized.
While the onions are cooking down, clean your chicken livers of any white or greenish fibers. These fibers are totally fine to eat, but cleaning them away will help the texture of your finished mousse.
Once the onions have cooked down add additional tablespoon of chicken fat and butter and raise the heat. Add livers and pink salt and cook, stirring and tossing them constantly for 5-7 minutes, or until they are firm to the touch but still rosy. If you have a meat thermometer the internal temp should be 165F. Generally, overcooking liver leads to an unappealing grainy texture, but the cream cheese and the blending/passing through a sieve will help cover all manner of overcooking sins, which makes this process way less stressful.
Once your livers are cooked, transfer them to a bowl. Deglaze your pan with the port and allow it to cook down slightly (about 1 minute). Pour port over livers and add cream cheese.
Place this mixture in a high-powered blender and blend until very smooth (you will have to do this in more than one batch).
Pass the puréed liver into a bowl through a fine mesh sieve. Once all of the liver has been passed through a sieve, add sugar, sherry vinegar, and salt to taste. Remember that this mousse’s flavor will change as it cools, so add a little more salt than you think tastes right. Also feel free to add more sherry vinegar, more sugar, and more pepper, etc.
Divide mousse into jars and coat the top in a thin layer of either rendered chicken fat or olive oil. This helps to seal the surface and keeps the liver from oxidizing and turning gray -- it also helps to keep it fresher for longer. Mousse will last 10 days in the refrigerator.