PARMESAN CUSTARD:

4 tbsp. butter
4 tbsp. flour
2 c. milk
1 c. chicken broth or stock
3 eggs
1/2 c. grated Parmesan cheese
1/2 tsp. salt, or to taste
Pinch of ground red pepper and ground nutmeg

9 plain lasagne noodles
2 tbsp. butter
1 c. chopped onion
1 clove garlic, minced
2 whole skinless and boneless chicken breasts (1 1/4 lbs.) cut into 1/4
inch strips
1 bag (1 1/4 lbs.) frozen broccoli cuts or chopped broccoli
1/2 c. shredded carrot
1/4 c. chopped Italian flat-leaf parsley
Salt and pepper to taste
1 lb. Mozzarella cheese, cut into thin slices
1/4 c. grated Parmesan cheese

To make the Parmesan custard, melt the butter in a medium saucepan; stir in the flour, over low heat, until smooth and golden, about 3 minutes. Stir in the milk; whisk over medium heat until smooth, about 5 minutes. Stir in chicken broth, about 10 minutes. Beat the eggs in a separate bowl; gradually whisk sauce into the eggs; return to saucepan and let stand off heat. Stir in cheese; season with salt, red pepper, and nutmeg.

Cook the lasagne noodles in plenty of boiling water until al dente, or firm to the bite, about 12 minutes; drain. Let noodles stand in a bowl of cool water until ready to use.

Melt the 2 tablespoons of butter in a large skillet. When foam subsides, add the onion; saute until golden, about 5 minutes. Stir in the garlic; saute 1 minute. Add the chicken strips and saute over medium heat until cooked through, turning as needed. Stir in the broccoli and carrot; cook covered, over medium heat just until vegetables are tender, about 5 minutes. Add parsley and season with salt and pepper.

Heat oven to 350 degrees F. Select a 9x13 inch shallow baking dish. Spoon about 1/2 cup of the Parmesan custard into the bottom of the dish. Lift the noodles from the water individually and blot dry on paper toweling. Arrange 3 noodles on the bottom of the dish.

Arrange half the chicken and broccoli mixture over the noodles. Drizzle with 1/2 cup of the Parmesan custard. Add a layer of one-third of the Mozzarella slices. Sprinkle with 1 tablespoon of the Parmesan. Arrange a second layer of 3 slightly overlapping lasagne noodles on top. Add the remaining chicken and broccoli mixture, half of the remaining Mozzarella, 1 tablespoon of the grated Parmesan, and 1/2 cup of the Parmesan custard.

Top with the remaining lasagne noodles. Arrange the remaining Mozzarella slices on top and carefully pour the remaining Parmesan custard over the top, pulling away the noodles along the sides of the dish so the sauce can seep down. Sprinkle with the remaining grated Parmesan. Bake until the top is browned and bubbly, about 50 minutes. Let stand at least 15 minutes before serving.