In a medium saucepan, boil rice in water 30 minutes. Drain, rinse, and set aside.
Meanwhile, in a large soup pot, melt butter over medium heat. Cook onion in butter until translucent. Stir in flour all at once to form a roux. Stir in broth, a little at a time, and cook until slightly thickened. Stir in carrots, ham, milk, parsley and reserved rice. Reduce heat and simmer 15 minutes.
Stir in vermouth and simmer 30 minutes more. Serve.