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