Preheat the oven to 350°F (175°C).
In a large skillet, heat olive oil over medium-high heat. Add ground beef and cook until browned, breaking it apart with a spoon, about 5-7 minutes. Drain excess fat and transfer beef to a large mixing bowl.
In the same skillet, add chicken pieces, season with salt, pepper, garlic powder, and onion powder. Cook until chicken is cooked through and no longer pink, about 6-8 minutes. Add cooked chicken to the bowl with beef.
Add diced ham, cooked egg noodles, and 1 cup of shredded Swiss cheese to the meat mixture. Stir to combine evenly.
In a medium saucepan, melt butter over medium heat. Whisk in flour and cook for 1-2 minutes until lightly golden, stirring constantly.
Gradually whisk in milk, continuing to stir until the sauce thickens and comes to a simmer, about 5 minutes.
Remove sauce from heat and stir in Dijon mustard, nutmeg, and remaining 1/2 cup shredded Swiss cheese until cheese is melted and sauce is smooth.
Pour the cheese sauce over the meat and noodle mixture and stir gently until everything is well coated.
Transfer the mixture to a greased 9×13 inch casserole dish and spread evenly.
Bake uncovered in the preheated oven for 30-35 minutes until bubbly and golden on top.
Remove from oven and let rest for 5 minutes before serving.