Mix broth with 1 cup of water in saucepan. add potatoes and bring to a boil over high heat; reduce heat to low, cover and simmer 10 to 15 minutes or until potatoes are fork tender.
Remove the cooked potatoes from broth, reserving the liquid. Puree cooked potatoes with 1/4 cup of broth. Add tuna, vegetables, seasonings, and pureed potatoes. Cover and heat to simmer for 8 to 10 minutes, until the fish flakes easily when tested with a fork.
Stir in the milk; heat to serving temperature (do NOT boil). Sprinkle with parsley just before serving.