Wash eggplant, remove the stem, peel (optional), and cut into thin rounds. Salt rounds generously on each, and leave for 20-25 min to releases juice. Dice onion, mince garlic, peel potatoes and cut into thin rounds. Boil 1-2 quarts water in a pot, and throw in potato rounds for 5 minutes. Take out, submerge in cold water and dry with paper towel. Heat oven to 450F. Place eggplant rounds on paper towel and press to expel more juices. Put a skillet over high heat so the pan is extremely hot, and after a minute add a dash of oil. Add eggplant rounds and brown (about 5 min each side). Remove rounds and place on paper towel to soak up extra oil. Add more oil to skillet, wait a minute, and then add onion and garlic. Once these crystalize, add ground beef, 1 tsp paprika, salt and pepper to taste, and mix well. Cook for additional 3-5 minutes. (Meat should still be somewhat pink.) Strain. Mix eggs and sour cream until smooth. Lightly grease a deep baking dish on all sides (I used 8x8). Start layering ingredients in starting with potatoes. The layers should go in this order: potatoes, ground beef, eggplant, cheese, eggplant, potatoes. Pour sour cream/ egg mixture on top. Sprinkle with remaining paprika and parsley. Place in oven on medium rack. Bring the oven temperature to 375F, and bake for 45-50 minutes, turning the baking pan once every 15 minutes. If the top starts to blush too much, or too soon, cover with foil and add a few minutes to the total baking time.