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Cook Buttery Chicken: Season raw chicken breast halves with salt and pepper. Heat 2 tablespoons of butter in pot over medium high heat. Add chicken and cook covered for approximate 6 minutes on each side. Remove chicken from pot and cut into small cubes or shred, and set aside for later.
Heat Buttery Ham: Heat 2 tablespoons of butter in pot over medium high heat. Add ham cubes and cook covered until butter starts to absorb, around 5-7 minutes.
Sauté Aromatics into a Butter-Flour Roux: Add onions, celery, garlic, salt and pepper, and paprika and cook covered until onions turn translucent, around 5-7 minutes. Add dijon and stir. Add flour, and cook until it turns pasty, around 1 minute.
Build the Broth: Return cooked chicken, add chicken broth and thyme. Bring the pot to a boil over high heat, stirring frequently, then reduce the heat to low and simmer, stirring occasionally, until flavors absorb, around 10-15 minutes.
Final Touch of Dairy: Increase heat to medium-low and add cream cheese, and Swiss cheese and cook, stirring frequently, until cheese is fully melted, around 5 minutes. Remove pot from heat, add heavy cream, stir, and serve 1-cup servings!