Heat the olive oil in a large skillet over medium-high heat for about 2 minutes. Add the chopped onions and cook for about 5 minutes, stirring occasionally, until softened.

Add the ground beef (or lamb) to the skillet, breaking it apart with a wooden spoon. Sprinkle in the dried parsley, rosemary, thyme, salt, and pepper. Stir thoroughly and cook for 6-8 minutes, until the meat is browned and cooked through, stirring occasionally.

Mix in the Worcestershire sauce and minced garlic, stirring well. Let it cook for another minute.

Add the all-purpose flour and tomato paste, stirring until fully incorporated and the mixture is smooth.

Pour in the beef broth, then add the frozen peas, carrots, and corn. Stir to combine, bring to a boil, then reduce to a simmer. Let it simmer for about 5 minutes, stirring occasionally, until the mixture thickens slightly.

Set the meat mixture aside and preheat your oven to 400 degrees F.

Place the cubed potatoes in a large pot and cover with water. Bring the water to a boil, then reduce to a simmer. Cook until the potatoes are tender and easily pierced with a fork, about 10-15 minutes.

Drain the potatoes in a colander, then return them to the hot pot. Let the potatoes sit for a minute to evaporate any remaining moisture.

Add the unsalted butter, half & half, garlic powder, salt, and black pepper to the potatoes. Mash until smooth and creamy, making sure all ingredients are well mixed.

Fold in the grated parmesan cheese, stirring until fully incorporated.

Spread the meat mixture evenly in a 9x9 (or 7x11) inch baking dish. Layer the mashed potatoes on top, smoothing them out to cover the meat evenly.

If your baking dish is quite full, place it on a rimmed baking sheet to catch any overflow during baking. Bake the casserole, uncovered, for 25-30 minutes, until the top is golden and the filling is bubbling around the edges. Let it cool for 15 minutes before serving.