01 - Preheat oven to 400°F. Lightly grease a 9x13-inch casserole dish with butter or nonstick spray.
02 - Bring a large pot of salted water to a rolling boil. Add the trimmed and halved Brussels sprouts, cooking for 3 to 4 minutes until just tender-crisp. Drain thoroughly and set aside.
03 - In a large skillet over medium heat, melt the butter. Add the chopped onion and cook until softened and translucent, about 3 minutes. Stir in the minced garlic and cook for an additional 30 seconds until fragrant.
04 - Sprinkle the flour over the onion and garlic mixture. Stir continuously and cook for 1 to 2 minutes to form a smooth roux, removing any raw flour taste.
05 - Gradually whisk in the whole milk and heavy cream, pouring slowly to prevent lumps. Continue whisking over medium heat until the sauce thickens and coats the back of a spoon, approximately 4 minutes. Stir in the Dijon mustard, salt, black pepper, and ground nutmeg.
06 - Remove the skillet from heat. Add ¾ cup of the Parmesan cheese and all of the mozzarella cheese, stirring gently until completely melted and the sauce is smooth.
07 - Add the blanched Brussels sprouts to the skillet, tossing gently to coat evenly with the creamy cheese sauce. Transfer the entire mixture into the prepared casserole dish, spreading it into an even layer.
08 - Sprinkle the remaining ½ cup of Parmesan cheese evenly over the top. In a small bowl, toss the panko breadcrumbs with the olive oil, then scatter the mixture over the casserole for a golden, crunchy finish.
09 - Bake in the preheated oven for 25 to 30 minutes, or until the top is deeply golden and the sauce is bubbling around the edges.
10 - Remove the casserole from the oven and allow it to rest for 5 minutes. Garnish with freshly chopped parsley and serve hot.