Preheat oven to 300 degrees F.
Saute the Mushrooms: In a saucepan, melt 1 tablespoon of butter. Add the shitake mushrooms and saute for 1 minute, until soft and cooked through. Add chopped parsley. Add Cognac and let simmer for 30 seconds. Remove mixture to a bowl and set aside.
Cook the Onion: Wash the saucepan and put back on stove. Add 2 tablespoons of butter on medium heat. When the butter starts bubbling, turn the heat down to low and add the onions. Cover and cook 5 minutes, stirring occasionally. The onions should be soft and translucent. Add the garlic, salt and pepper. Saute until garlic is fragrant. Add the cream and bring to simmer. Cover and cook for 5 minutes. Add all of the remaining butter. Stir until melted. Turn off the heat.
Puree the Liver: Put livers in a blender. Pulse a few times until the liver becomes a little smoother. Add the onion mixture. Puree on high for 2 minutes until the mousse becomes pale color and totally smooth. Strain the mixture, using the back of a spoon to push through. You should have about 3 cups strained mousse. If you don't have that much, put the solids back in the blender and puree again.
Bake the Pate: Add the shitake/cognac mixture into the strained mixture. Stir to incorporate the mushrooms evenly throughout the mousse. Pour into 4 1-cup ramekin dishes. Cover with aluminum foil and place in a large deep baking dish. Make sure the bowls don't touch each other. Carefully pour in enough boiling water to reach halfway up the sides of the ramekins. Bake 30 minutes. Remove from oven and let cool to room temperature. Refrigerate to chill. Once it is chilled, you can prepare the gelee.