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Peel the potatoes and chop into coarse pieces. Cook the potatoes in a medium-sized pan, the exact time depends on the type of potatoes and size of the pieces. Meanwhile peel the pumpkin, remove the seeds and divide in chunks.
Cook the pumpkin in boiling water until it's softened enough to create a puree. Peel the carrot and divide into small cubes. Peel and finely chop the onion and garlic cloves.
Heat a bit of olive oil in a skillet and sauté the onion, garlic and carrot for a few minutes. Add the ground beef and cook a few minutes more.
Season with pepper and salt and divide the mixture over the bottom of the oven dish.
Drain the pumpkin pieces and create a puree, you can use an immersion blender or press the pumpkin through a fine sieve. Season the puree with pepper and salt and make sure it's as dry as possible.
Divide the pumpkin puree over the ground beef mixture. Pre-heat the oven to 180 degrees Celsius or 350 degrees Fahrenheit. Drain the potatoes and also create a puree of the potatoes.
Add a bit of butter, milk and cream to create a smooth puree. Season with pepper, salt, a pinch of nutmeg and a handful of grated cheese.
Divide the mashed potatoes over the pumpkin puree and finish it off with another handful of grated cheese.
Bake the parmentier in the oven for about half an hour, or until the cheese is beautiful golden brown. Enjoy!