Melt butter in a large pot over medium heat. Add diced onion and sauté until translucent, about 5. Add minced garlic and cook for an additional 1.

Sprinkle flour over the onion and garlic mixture. Stir constantly for about 2 to create a roux. Gradually whisk in chicken broth and bring to a gentle simmer. Stir in shredded chicken and let it simmer for about 10.

Stir in diced ham and dried thyme. Reduce heat to low and stir in heavy cream and Dijon mustard. Add shredded Swiss cheese and stir until melted.

Blend the soup with an immersion blender for a smoother texture, if desired.

Season with salt and pepper to taste. Serve hot in bowls, garnished with chopped fresh parsley.