In a small bowl, combine cottage cheese and cream cheese; set aside. In another bowl, combine the next six ingredients; set aside.
Place 2 lasagna noodles in a greased 11x7-in. baking dish. Top with half the cottage cheese mixture and a third of the broccoli mixture. Repeat layers of noodles, cheese and broccoli. Top with 2 noodles, chicken and remaining broccoli mixture. Sprinkle with Monterey Jack cheese. Pour boiling water around edges of dish.
Cover tightly and bake at 350° for 60-65 minutes. Leave covered and let stand for 10 minutes before serving.