In large pot of boiling salted water, cook lasagna until tender but firm; drain and refresh with cold water.
Set aside on paper towels.
In shallow saucepan, bring sole and milk to simmer; cook, covered, for 5 minutes or until fish flakes easily when tested with fork.
Drain well, reserving hot milk.
Meanwhile, peel and slice broccoli stalks; divide florets into bite-size pieces.
In large pot of boiling salted water, cook broccoli for 2 minutes; drain and refresh under cold water.
Drain well and set aside on paper towels.
In saucepan, melt butter over medium heat; cook mushrooms for 3 to 5 minutes or until softened.
Add flour; cook, stirring, over low heat for 2 minutes without browning.
Remove from heat.
Stir in reserved hot milk, salt, pepper and nutmeg; cook over medium heat, stirring, until thickened.
Reduce heat to low; gradually stir in cream.
Remove from heat.
Taste and adjust seasoning.
Stir in 1 cup (250 mL) of the Swiss cheese.
Lightly spread some of the sauce in greased 13- x 9 inch (3 L) glass baking dish.
Flake sole; stir sole and shrimp into sauce in pan.
Arrange 3 lasagna noodles in dish; spoon thin layer of sauce over top, spreading carefully to cover noodles.
Arrange broccoli on top; dot with a few tablespoons of sauce.
Stir 1/4 cup (125 mL) of the Parmesan into remaining Swiss cheese; sprinkle half over broccoli.
Top with 3 more noodles; top with remaining sauce.
Sprinkle with remaining cheese mixture; top with remaining Parmesan.
(Recipe can be prepared to this point, covered and refrigerated for up to 8 hours.) Cover with foil; bake in 350°F (180°C) oven for 30 minutes.
Uncover and broil for about 2 minutes or until golden brown on cop.