Heat the butter in a soup pot over medium-high heat and cook the onion, carrot and celery until softened, about 10 minutes. Add the mushrooms and garlic and cook for another 5 minutes. Sprinkle the flour over the mixture and stir to combine, cooking for another 2 minutes. Pour in the broth and wine and stir in the rice, thyme, ground mustard, salt and pepper. Bring to a boil, reduce the heat to medium-low, cover and simmer for 30 minutes. Add the ham, cover and simmer for another 15 minutes or until the rice is tender. Stir in the cream and parsley and heat through. Add salt and pepper to taste.
Serve immediately.
Notes
Leftover soup will become thick as the rice expands. If it's too thick simply dilute with a little broth.