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RINSE the eggplants and divide them into long not too thin strips. SEASON with salt and place them in a colander, the salt will extract the moisture from the eggplant.
FILL a small pan with water and salt and bring to a boil. PEEL the potatoes and chop them into thin slices. COOK them in the boiling water for a few minutes and then drain them.
Meanwhile PEEL the onion and garlic cloves, CHOP the onion into thin half rings and finely chop the garlic. HEAT olive oil in a large skillet and sauté the onion and garlic for a few minutes.
ADD tomato paste and cook it some more. COOK the paprika powder also very shortly before you add the oregano and canned tomatoes. ADD a dash of water and let the sauce simmer for a few minutes. SEASON with pepper and salt and set aside.
PAT the eggplant slices dry using paper kitchen towels. HEAT a grill pan on high heat and drizzle the eggplants with olive oil. GRILL them on both sides until the grilling pattern appears.
SEASON the slices immediately with pepper and salt and REPEAT until all the slices are grilled. HEAT the oven to 180 degrees Celsius or 350 degrees Fahrenheit and coat the oven dish with butter.
Start with a layer of grilled eggplant, than a layer of potato slices and tomato sauce. DIVIDE a bit of grated cheese before you'll start with another layer of eggplant, potatoes and tomato sauce.
End with a layer of eggplant and the rest of the grated cheese. DIVIDE a small handful of panko and some small knobs of butter on top of the gratin and BAKE in the oven for about 30 minutes, or until the cheese is beautiful golden brown. Enjoy!