Make the mashed potatoes: place the cubed potatoes in a large pot of water. Bring to a boil and cook until fork tender, about 15 mins. Drain and return the potatoes to the pot.
Mix in the half and half, butter, salt, and pepper and mash using a potato masher until creamy and smooth. Set aside.
Make the meat filling: heat the oil in a large Dutch oven over medium-high heat and saute the onions, garlic, carrots, and celery for about 5 minutes. Add the ground beef and cook until there’s no more pink left in the meat, about 8 more minutes.
Mix in the tomato paste, Worcestershire sauce, dried herbs, salt, pepper, and chicken broth. Simmer this mixture until the sauce is slightly thickened, about 5 minutes. Remove from heat and add the frozen peas.
While the meat filling is simmering, preheat the oven to 400 F.
Assemble the Pie: Flatten the meat mixture using a spatula and spoon the mashed potatoes on top. Smooth them over with the spatula as well, and bake for 25 minutes. Turn on the broiler and broil for 2-5 minutes or until golden brown on top. Watch them carefully as food can easily burn if left unsupervised under the broiler! Serve with freshly chopped parsley on top.