Heat olive oil in a large skillet over medium-high heat for about 2 minutes. Sauté the chopped onion for 5 minutes, stirring occasionally. Add the ground meat, breaking it apart with a spoon. Sprinkle in parsley, rosemary, thyme, salt, and pepper. Cook for 6-8 minutes, stirring occasionally, until the meat browns. Incorporate Worcestershire sauce and garlic, stirring to combine. Cook for an additional minute. Mix in the tomato paste and flour until fully blended. Stir in beef broth, peas, carrots, and corn, bringing the mixture to a boil before reducing to a simmer. Cook for 5 minutes, stirring occasionally. Set aside and preheat the oven to 400°F.

Place the potato cubes in a large pot and cover them with water. Bring to a boil, then reduce to a simmer. Cook for 10-15 minutes, or until the potatoes are fork-tender. Drain using a colander and return the potatoes to the hot pot, allowing them to rest for 1 minute to remove excess moisture. Mash the potatoes with butter, half & half, garlic powder, salt, and pepper until smooth. Stir in the parmesan cheese until fully incorporated.

Transfer the meat filling into a 9x9-inch or 7x11-inch baking dish, spreading it evenly. Top with the mashed potatoes, smoothing them into an even layer. If the dish is very full, place it on a rimmed baking sheet to catch any overflow. Bake, uncovered, for 25-30 minutes at 400°F. Let the Shepherd's Pie cool for 15 minutes before serving.