1.Preheat oven to 180°C/530°F. Oil 1.5-litre (6-cup) ovenproof terrine dish.
2.Line base and sides of dish with prosciutto slices, allowing 7cm (2½-inch) overhang on long sides of dish.
3.Heat 1 tablespoon of the oil in large frying pan; cook onion and garlic, stirring, until onion softens. Stir in cream; transfer to medium bowl.
4.Heat 1 tablespoon of the remaining oil in same pan; cook mushrooms, stirring, until browned. Stir in cheese; transfer to another medium bowl.
5.Heat remaining oil in same pan; cook liver, stirring, over high heat, about 2 minutes or until browned, but not cooked through. Drain on absorbent paper.
6.Add liver and chicken to onion mixture in medium bowl; stir to combine. Spread one-third of the chicken mixture in terrine dish; arrange asparagus on top. Cover with another third of the chicken mixture; top with mushroom mixture, then top with remaining chicken mixture. Fold prosciutto slices over to cover chicken mixture.
7.Bake terrine about 1 hour or until chicken is cooked through. Remove from oven; drain juices from dish. Stand 20 minutes in dish before slicing.