01 - Preheat oven to 375°F. Grease a 9x13-inch baking dish and set aside.
02 - In a small bowl, combine the softened butter, minced garlic, chopped parsley, dill (if using), salt, black pepper, and lemon juice. Mix thoroughly until all ingredients are evenly incorporated. Set aside.
03 - Heat olive oil in a large skillet over medium-high heat. Season the chicken pieces lightly with salt and pepper, then add to the skillet. Sauté for 5 to 7 minutes until just cooked through and lightly golden on the edges. Transfer the seared chicken to the prepared baking dish in an even layer.
04 - In the same skillet, sprinkle the flour over the residual drippings and cook for 1 minute, stirring constantly to form a roux. Gradually whisk in the whole milk and chicken broth, ensuring no lumps remain. Bring the mixture to a simmer and cook for 3 to 4 minutes until the sauce thickens enough to coat the back of a spoon.
05 - Remove the skillet from heat. Whisk the prepared garlic-herb butter into the sauce until completely smooth and emulsified. Pour the finished sauce evenly over the chicken in the baking dish.
06 - In a medium bowl, combine the breadcrumbs, grated Parmesan cheese, and melted butter. Toss until the crumbs are evenly coated. Sprinkle the mixture in an even layer across the top of the casserole.
07 - Bake uncovered on the center rack for 25 minutes, or until the topping is deeply golden and the sauce is bubbling around the edges.
08 - Remove the casserole from the oven and allow it to rest for 5 minutes. Garnish with fresh chopped parsley and serve warm.