Combine milk, cognac, and morel mushrooms in a bowl; soak for 20 minutes.
Preheat the oven to 350 degrees F (180 degrees C). Grease a terrine mold.
Combine chicken livers, ham, and garlic in a food processor. Process until mixture is smooth and well combined. Add ground pork, egg, pepper, and salt. Process again until smooth and well combined.
Drain morel mushrooms and and chop; stir mushrooms into the meat mixture. Tip pate mixture into the prepared terrine mould. Smooth out mixture with the back of a spoon and gently press bay leaf on top.
Bake in the preheated oven until pate has set, about 1 hour. Remove from oven and allow to cool to room temperature. Chill in the refrigerator for at least 6 hours before serving