Place corned beef in a large saucepan with enough cold water to cover it by 2 inches; add TABASCO® Green Sauce. Bring to a boil over high heat; reduce heat to low, cover, and simmer 2 hours, skimming foam off surface occasionally.
Add cabbage to broth in saucepan during last 10 minutes of cooking and return to boiling over high heat. Reduce heat, cover, and simmer 10 minutes or until cabbage is tender. Remove corned beef and cabbage to a warm serving platter, reserving broth. Keep beef and cabbage warm while preparing dumplings.
For dumplings, combine flour, baking powder, and salt in a medium bowl. Whisk milk, egg, parsley, butter, and TABASCO® Green Sauce in another bowl until blended. Stir milk mixture into dry ingredients.
Bring reserved broth to a simmer. Drop batter by tablespoons into broth; cover and simmer 10 minutes or until dumplings are cooked in center. Using a slotted spoon, transfer dumplings to a platter with corned beef and cabbage. Serve immediately.
Makes 6 to 8 servings.