White Lasagna with Chicken and Satueed Mushrooms

I thought this had great flavor and wasn't too rich since I used 2% milk and there's not much cheese. It's a pretty good base for any additional ingredients --like prosciutto, spinach, diced roma tomatoes.... I think it's a good balance between the food I like and the comfort food that Taylor is partial too.

White Lasagna with Chicken and Sauteed Mushrooms
adapted from Gourmet
INGREDIENTS
3/4 cup minced shallots (about 6)
8 tablespoons unsalted butter
1/2 cup all-purpose flour
1/2 teaspoon grated nutmeg
3 3/4 cups whole milk (I used 2%)
1 cup rich chicken stock or reduced-sodium chicken broth
2 large eggs, lightly beaten
1/2 teaspoon salt
2 cups grated Parmigiano-Reggiano, divided
12 (7- by 3-inch) no-boil egg lasagna sheets
2 cups shredded rotisserie chicken
1 cup sauteed sliced mushrooms
DIRECTIONS
Preheat oven to 350°F with rack in middle.
Cook shallots in butter in a heavy medium saucepan over medium heat, stirring occasionally, until tender, about 4 minutes. Add flour and cook over low heat, stirring with a wooden spoon, 3 minutes. Add nutmeg, then slowly whisk in milk and stock. Bring to a boil, whisking, then simmer, stirring occasionally, just until sauce lightly coats back of spoon, about 1 minute. Remove from heat and cool to warm, stirring occasionally. Stir in eggs, salt, 1/2 teaspoon pepper, and 1/2 cup cheese.

Spread about 1 1/4 cups sauce over bottom of an 11- by 8-inch baking dish. Cover with a layer of 3 lasagna sheets. Coat sheets in about 1 1/4 cup sauce, sprinkle with cheese, mushrooms and chicken. Repeat layering 3 more times, then top with remaining sauce and remaining 1/2 cup cheese. Bake, uncovered, until browned, 45 to 55 minutes.

Sauce can be made 1 day ahead and chilled, covered (once cool).

Update {07/13}: I halved this recipe but thought that I needed to up the flour to compensate for the less thick 2% milk. Such is not the case, equal parts butter (fat) and flour is the base of this type of sauce. Then add and stir liquids to desired consistency. Halving it should not be a problem.