Melt butter in a large pan over medium high heat. Add chicken and cook for 3-4 minutes. Add onion and garlic and cook for 3 more minutes. Add flour. Cook and stir for at least 1 minute.
Add chicken broth, cream, 1/4 cup Parmesan, mustard, thyme, salt, pepper, and broccoli. Reduce heat and simmer for 5-6 minutes. Stir in ham and heat through.
Spoon mixture into bread bowls that have been placed on a foil lined cookie sheet. Sprinkle with parmesan cheese, then mozzarella.
Place on the top rack of the oven, and broil for about 4 minutes, or until cheese starts to brown. Serve immediately.