Melt the butter in a large stockpot over medium heat.
Add the diced onion, carrots, celery, minced garlic, paprika, salt, and pepper; cook while stirring regularly until the carrots have softened, about 10 minutes.
Pour in the chicken broth, heavy cream, and Dijon mustard, then add the cooked and cubed chicken, turkey ham, and the cubed cream cheese; cook while stirring regularly until the soup is hot and the cream cheese has melted.
Taste the soup and adjust the seasoning if necessary.
Serve the soup hot, topped with shredded Swiss cheese and croutons.