In a large pot, melt the better on low heat and add the diced onion. Cook onion in butter until onion is soft, about 2-3 minutes. Add the garlic and cook for 30 seconds. Add the flour and cook for one minute.
Slowly whisk in the chicken broth and half-and-half. Add the cream cheese and stir until combined. Stir in Swiss cheese until melted. Stir in the chicken and ham until heated through. Serve.
Notes
For the chicken broth: I really like the flavor of Better than Bouillon Chicken Base with water added to as called on the package.You can substitute half cream and half milk for the half-and-half.