Prep Time: 90 minutes
In a large pot over a medium flame, heat the oil until hot. Add the onion and carrot and stir for about 6 minutes, until the onion is translucent and the carrot is slightly tender. Meanwhile, bring a large pot of salted water to a boil over a high flame. Boil the parsnips until fork tender, about 20 minutes. Drain and return to the pot, adding the cream and butter. Cover and set aside. Preheat the oven to 400 degrees.
When the vegetables are cooked, add the ground beef and stir until slightly browned and most of the moisture is cooked off, about 15 minutes. Add the tomato paste and vegetable broth along with a pinch of salt and pepper and stir for 2 minutes. Set aside.
Using a hand blender or potato masher, mash the parsnips until smooth. Season with a pinch of salt and pepper to taste. Pour the beef and vegetable mixture into the bottom of a greased casserole dish. Cover with the mashed parsnips evenly, creating peaks with the back of a spoon. Place into the oven for 30-45 minutes, rotating once, until the parsnips are browned. Divide evenly between 4 plates.