Melt butter in a Dutch oven or large pot. Add cream cheese to melted butter and melt.
Add ham and heavy cream to melted butter and cream cheese. Stir to combine.
To the ham add chicken and three cups of the chicken broth. SImmer on low for 5-10 minutes. Stirring occasionally.
Stir in 1 cup of shredded Swiss cheese and continue to stir until the cheese is melted. If the soup isn't as liquidy as you like it, add the additional cup of broth. Finally, add salt and pepper and parsley.