Add olive oil to a large skillet set over medium-high heat and heat for 2 minutes. Sauté the chopped onion for approximately 5 minutes, stirring now and then. Incorporate the ground beef or lamb, breaking it up with a wooden spoon. Stir in parsley, rosemary, thyme, salt, and black pepper. Continue to cook for 6–8 minutes until the meat is browned.

Introduce Worcestershire sauce and minced garlic to the pan, stirring thoroughly, and cook for an additional minute. Mix in the tomato paste and flour, ensuring they are fully blended and free of lumps. Pour in the beef broth, followed by the mixed peas and carrots and corn kernels. Bring to a boil, then lower the heat and let it simmer for 5 minutes, stirring occasionally. Set the finished meat mixture aside. Preheat the oven to 400°F.

To prepare the mashed potato topping, place the cubed potatoes in a large pot and cover with water. Bring to a boil, reduce to a simmer, and cook until fork-tender, about 10–15 minutes. Drain and return the potatoes to the pot, allowing them to sit for 1 minute to eliminate excess moisture. Add butter, half & half, garlic powder, salt, and pepper. Mash and stir until well blended, then mix in the parmesan cheese.

Spoon the meat mixture evenly into a 9x9 or 7x11 inch baking dish. Layer the mashed potatoes over the top, spreading gently to create a smooth surface. If the dish is quite full, place it on a rimmed baking sheet to prevent spills. Bake uncovered for 25–30 minutes. Allow to cool for 15 minutes prior to serving.