Melt the butter in your large pot over medium heat until it begins to bubble and sizzle. Add the diced onion, carrots, and celery and sauté for five minutes until they are soft and fragrant.

Stir in the minced garlic and cook for just one minute so it does not burn and turn bitter. The garlic provides a wonderful aromatic base that pairs perfectly with the salty ham and creamy Swiss cheese.

Whisk the all-purpose flour into the buttery vegetable mixture until a thick, golden paste forms in the pot. Cook the flour for two minutes to remove the raw taste before adding any liquid to the pot.

Slowly pour in the chicken broth while whisking constantly to prevent any lumps from forming in your soup. Bring the mixture to a gentle boil until the broth begins to thicken into a light gravy consistency.

Stir in your diced chicken and the salty ham cubes into the bubbling broth mixture in the stockpot. The flavors of the meat will start to meld with the savory vegetables and the thick, buttery base.

Reduce the heat to low and slowly stir in the heavy whipping cream and the Dijon mustard. The cream adds a beautiful white color and a rich, luxurious mouthfeel that makes this soup feel very special.

Add the shredded Swiss cheese one handful at a time, stirring constantly until the cheese is completely melted. Adding it slowly ensures the soup remains smooth and does not become grainy or clumpy during the process.

Stir in the dried thyme, salt, and black pepper to perfectly balance the rich and creamy flavors. Taste a small spoonful to see if it needs more mustard or a little extra pinch of salt.

Let the soup simmer on low heat for ten minutes to allow all the delicious flavors to combine perfectly. Do not let it boil vigorously once the cream and cheese are added to avoid any curdling.

Ladle the hot soup into deep bowls and top with crispy croutons or a sprinkle of fresh parsley. Serve immediately while the cheese is still melty and the chicken is perfectly tender and warm.