Melt the butter in a large stockpot over medium heat. Add onion, carrots, celery, garlic, paprika, salt, and pepper. Cook until the carrots are tender, stirring occasionally.
Pour in the chicken broth, heavy cream, and Dijon mustard. Stir to combine, allowing the flavors to meld together.
Mix in the cubed chicken, ham, and cream cheese. Stir until the cream cheese fully melts and the soup becomes creamy and smooth.
Taste the soup and adjust seasoning if needed. Serve hot with shredded Swiss cheese and croutons on top for extra flavor and crunch.