Place hamburger, onion, garlic, parsley, rosemary, thyme, salt, and pepper in a large skillet on medium heat; break up hamburger and stir until the beef is browned and vegetables are softened (if hamburger has high fat content, drain excess fat before proceeding).
Add the Worcestershire sauce, flour and tomato paste; stir well.
Add broth, peas, carrots, and corn. Bring to a bubbly boil; reduce heat and simmer uncovered ~5 minutes, stirring occasionally; set aside.
Place cubed potatoes in a kettle ½ full of boiling water; cook until tender (~5 minutes); drain and return to warm kettle.
Add butter, half& half, garlic powder, salt, and pepper. Mash the potatoes and mix well. Add the Parmesan cheese; stir until well combined.
Pour the meat mixture in a casserole or small baking dish. Spread into an even layer. Spoon on the potatoes; carefully spread into an even layer.
Bake uncovered for 25 minutes. Cool for 15 minutes before serving.