Melt butter in a large pot over medium heat. Add chopped onion and garlic. Cook until soft and fragrant. Stir often to prevent burning and ensure even cooking.

Add flour to the pot. Stir constantly for about one minute. This helps remove raw flour taste. The mixture will become thick and slightly golden.

Slowly pour in chicken broth while whisking. This prevents lumps from forming. Keep stirring until the mixture becomes smooth and starts to thicken slightly.

Pour in milk and heavy cream. Stir well to combine. Let it simmer gently. The soup will become creamy and smooth with a rich texture.

Add shredded chicken and diced ham to the pot. Stir gently. Let it cook for a few minutes so the flavors blend nicely together.

Add Swiss and cheddar cheese slowly. Stir until fully melted. The soup will become thick, creamy and cheesy. Make sure the heat is low to avoid curdling.

Add Dijon mustard, salt, pepper and paprika. Stir well. Taste and adjust seasoning if needed. These spices bring out the classic cordon bleu flavor.

Let the soup simmer for 5–10 minutes. Stir occasionally. This helps all flavors blend together and gives a rich, comforting taste.

Turn off heat and let the soup rest for a few minutes. Serve hot in bowls. Garnish with fresh parsley for color and freshness.