In a 10- to 12-inch ovenproof nonstick frying pan over high heat, combine ground beef, onions, carrots, vinegar, and 1/2 cup broth. Stir often until meat is crumbled and carrots are tender when pierced, about 15 minutes. Spoon out and discard any fat.
Meanwhile, in a 2-quart microwave-safe bowl, combine potatoes and milk. Cook in a microwave oven at full power (100%) until hot and smoothly blended, 8 to 10 minutes, stirring every 2 to 3 minutes. Stir cheese and horseradish into potatoes.
Blend remaining broth and the cornstarch until smooth. Add broth mixture, peas, and marjoram to frying pan. Stir until mixture boils. Remove from heat.
Spoon mashed potatoes in dollops around edge of pan over beef mixture, leaving center exposed.
Broil 6 to 8 inches from heat until potatoes are lightly browned, about 8 minutes. Spoon onto plates.