Cut apricots in half crosswise.
Rinse and drain mushrooms. Trim off stems flush with caps. Finely chop stems and set caps aside.
In a 4- to 5-quart nonstick pan over high heat, frequently shake pine nuts until lightly browned, about 2 minutes. Pour into a small bowl.
To pan, add chopped mushrooms, oil, onion, and curry powder. Stir over high heat until mushrooms and onion are limp and juices evaporate, about 3 minutes. Remove from heat and spoon half the mixture into a large bowl.
To mushroom mixture in the pan, add apricots, bulgur, and 5 cups broth. Bring to a boil, stir, cover, remove from heat, and let stand until bulgur is tender to bite, at least 8 minutes.
Meanwhile, combine reserved onion-mushroom mixture, 1/3 cup broth, lamb, and bread crumbs. Mix well. Pat an equal amount of lamb mixture onto the cup side of each mushroom cap, covering evenly. Scatter 1 tablespoon pine nuts onto each meat-filled mushroom and gently press nuts into meat.
Divide the curried bulgur mixture equally between 2 casseroles, each 3 quarts (about 9 by 13 in. and at least 2 in. deep).
Lay 4 mushrooms, meat side up, in each casserole (they can overlap slightly). If making ahead, cover and chill up to 1 day.
Bake, covered, in a 400° oven until lamb mixture is no longer pink in center (cut to test, or if chilled, it should register 150° on a thermometer; see notes), 35 to 40 minutes (about 1 hour and 10 minutes if chilled).
Mix yogurt with mint. If making ahead, cover and chill up to 1 day.
Spoon portions onto plates and add yogurt sauce and salt to taste.