• Boil the potatoes in their skins until fork-tender. Let them cool completely, then peel them and set them aside for later.
  
• Finely dice the onion and add it to a heavy-bottomed pot or deep pan with the oil.
  
• Dice the carrot into small cubes and add it to the pot with the onion.
  
• Finely chop the garlic cloves and add them to the pot.
  
• Place the pot over low heat and sauté the vegetables for 5–7 minutes, stirring often, until they soften without browning.
  
• Add the ground chicken to the pot.
  
• Season with salt, ground black pepper, paprika and dried thyme, then mix well to combine everything evenly.
  
• Stir in the tomato paste. Mix well so the paste and spices coat the meat and vegetables evenly, then cook over low heat for about 5 minutes.
  
• Pour in the water, cover the pot with a lid and let the meat simmer over low heat for another 20–25 minutes.
  
• Prepare a baking dish by lining it with parchment paper and lightly greasing the top with a bit of oil. Slice the boiled potatoes into rounds and arrange the first layer of potato slices in the dish.
  
• Add the first layer of the cooked meat and vegetable mixture on top. To make it easier to layer evenly, divide the meat filling in the pot into two equal portions and use one portion for this layer so you have enough for the second layer later.
  
• Add a second layer of potato slices on top, arranging the potatoes in rounds again.
  
• Add the remaining half of the meat mixture as the fourth layer.
  

For the sauce:

• Grate the cheese, then add it to a bowl together with the sour cream and the egg. Mix until you have a smooth topping.
  
• Pour this sauce over the top of the final layer in the baking dish.
  
• Spread the sauce evenly with the back of a spoon. Bake the moussaka in a preheated oven at 340°F (170°C) for 25–30 minutes, until the top is set and lightly golden.
  
• Slice the potato moussaka and enjoy this hearty and comforting dish while warm.