01 - Preheat oven to 400°F. Grease a medium baking dish (about 2 quarts) with butter or nonstick spray.
02 - Heat olive oil in a large skillet over medium heat. Add chicken pieces, season with salt and pepper, and sauté until lightly browned on the outside but not fully cooked through, about 4-5 minutes. Transfer to a plate and set aside.
03 - In the same skillet, melt the butter. Add the diced onion and sauté for 2 minutes until translucent. Stir in the minced garlic and cook for 1 additional minute until fragrant.
04 - Sprinkle flour into the skillet and cook, stirring constantly, for 1 minute. Gradually whisk in the chicken broth, followed by the heavy cream and lemon juice. Continue cooking and stirring until the sauce thickens, about 3 minutes.
05 - Remove the skillet from heat. Stir in the dried thyme, ground nutmeg, half of the Parmesan cheese, and half of the mozzarella cheese. Mix until the cheese is fully melted and the sauce is smooth.
06 - Fold the seared chicken pieces and trimmed asparagus into the sauce, tossing gently until everything is evenly coated.
07 - Transfer the mixture into the prepared baking dish. Sprinkle the remaining mozzarella and Parmesan evenly over the top. Finish with a layer of breadcrumbs if desired.
08 - Bake in the preheated oven for 25-30 minutes, or until the chicken is cooked through, the asparagus is tender, and the top is golden brown and bubbling.
09 - Remove from the oven and let the casserole rest for 5 minutes before serving to allow the sauce to set.