White Sauce: In 3-quart saucepan, melt butter over medium-low heat. Add flour all at once and stir until blended; cook 2 minutes. Slowly add milk, whisking until smooth; sauce at first will become thick, then it will gradually loosen up. Increase heat to medium, stirring constantly, until sauce comes to a simmer. Stir in salt, pepper and nutmeg; simmer 4 minutes more. Remove from heat. (Sauce can be prepared ahead. Pour into bowl; place piece of plastic wrap directly on surface and refrigerate for up to 2 days. Let come to room temperature before using.)

Mushroom Filling: In large skillet, melt butter over medium-high heat. Add onion; cook, stirring occasionally, until softened, 5 minutes. Stir in mushrooms, salt and pepper; cook, stirring frequently, until all the liquid evaporates and mushrooms are tender, about 12 minutes. Remove from heat. Stir in spinach and carrots.

Heat oven to 375 degrees F.

Lasagna: Spread 1 cup white sauce over bottom of 13 x 9 x 2-inch lasagna pan. Set aside 1 cup white sauce. Stir remaining white sauce into mushroom mixture.

Arrange 4 lasagna sheets on top of sauce. Spread with half the mushroom mixture. Sprinkle with 1/2 cup cheese. Repeat layering, ending with sheets. Spread 1 cup sauce over top, spreading to cover pasta completely. Cover with foil.

Bake in 375 degree F oven 45 minutes. Uncover; sprinkle with remaining 1/2 cup cheese. Bake 15 minutes more or until browned and bubbling around edges. (If desired, run lasagna under broiler 2 minutes to brown and crisp top.) Let stand 10 minutes before serving. Cut into rectangles to serve. Makes 12 servings.