In a large pot, heat 2 tablespoons of olive oil over medium heat. Add the diced onion, chopped carrots, and sliced celery. Cook for about 5-7 minutes until the vegetables are softened and fragrant, stirring occasionally to ensure even cooking.

Next, stir in 1 cup of sliced cremini mushrooms and 2 minced garlic cloves into the pot. Continue to cook for another 3-5 minutes until the mushrooms are browned and tender.

Sprinkle ¼ cup of all-purpose flour over the sautéed vegetables. Stir well for about 1 minute to eliminate lumps and ensure the flour is fully incorporated.

Gradually whisk in 4 cups of chicken broth and 1 cup of heavy cream. If using, add ½ cup of dry white wine. Season with 1 teaspoon of dried thyme, ½ teaspoon of dried rosemary, a pinch of nutmeg, and salt and pepper to taste. Simmer for 15 minutes.

While the soup simmers, heat another skillet over medium heat and melt 2 tablespoons of butter. Add 1 pound of boneless skinless chicken breasts and cook for 5-7 minutes per side or until browned and cooked through. Remove the chicken, let it rest, and then dice it.

In the same skillet, add 1 cup of sliced cooked ham to warm it. Cook for around 2-3 minutes, stirring occasionally.

Add the diced chicken and warmed ham back into the pot with the soup base. Stir gently and let it simmer for an additional 5-10 minutes.

Finally, sprinkle in 1-2 cups of shredded Swiss cheese and stir until melted and smooth. Taste and adjust the seasoning.

Ladle the warm Chicken Cordon Bleu Soup into bowls and garnish with freshly chopped parsley. Serve hot.