Preheat the oven to 180 degrees Celsius/ 360 degrees Fahrenheit.
Chop the onions finely. Heat 1 tablespoon of the oil in a large heavy bottom pan or Dutch oven and fry the onions gently until they are translucent.
Add the ground meat and fry it until brown, stirring and breaking the lumps while it cooks.
In the meantime, peel the potatoes and slice them very thinly. Use a mandoline for this task, it guarantees for thin and regular potato slices which will cook evenly in the oven. Set aside.
When the meat is brown, add dried savory/thyme, sweet ground paprika, salt and pepper to taste.
Oil a medium, deeper casserole dish with a little of the remaining oil.
Divide the potato slices into 3 batches. Arrange the first batch of potatoes in a double layer into the dish. Sprinkle with salt and pepper. Cover with half of the ground meat.
Arrange another double layer of potato slices on top of that, adding salt and pepper again. Cover with the rest of the meat and add the last batch of potato slices. Sprinkle with salt and pepper again.
Mix the tomato puree with about 50 ml/ 1.7 fl.oz/ ¼ cup water to make it a bit runnier. Pour the mixture into the casserole dish. Add more water to barely fill the casserole dish, the upper layer of potatoes should not be covered in water though. Pour the remaining oil on top of the casserole.
Bake the potato moussaka for about 1 hour and 10 minutes or until the potatoes are soft. Check the potatoes and prolong the cooking time if they are not soft yet.
If the casserole dish gets too dark on top, cover it loosely with aluminum foil, you should check after about half the time and cover the dish if necessary.
Serve with pickled vegetables or salad.