Preheat broiler. In an extra-large skillet cook ground beef over medium-high heat until brown, using a wooden spoon to break up meat as it cooks. Drain off fat. Stir in frozen vegetables. Cook until mixture is heated through, stirring occasionally. Stir in 1 cup of the cheese, 2 tablespoons of the parsley, the 1/4 teaspoon salt, and the ground black pepper.
Meanwhile, in a large bowl combine the boiling water, potato flakes, and 1 tablespoon of the butter. Stir until smooth. Season with additional salt; set aside.
Divide meat mixture among four 16-ounce broiler-safe dishes. Top with potatoes; sprinkle with the remaining 1 cup cheese. Broil 3 inches from heat for 2 to 3 minutes or until cheese is melted. Drizzle with the remaining 1 tablespoon butter; sprinkle with the remaining 2 tablespoons parsley. Sprinkle with cracked black pepper.