Start by heating a splash of olive oil in a wide, metal skillet. When hot, add one layer of eggplant: don't crowd the pan (you may need to work in batches). Sear on all sides, then season with salt, and set aside. Do again until you've seared all the eggplant (you may need to add more oil as you go).
Add more oil to the pan (a few Tbs), and add the red onion. Season with salt and fry until golden brown. Add the garlic and cook just until it starts to color. Add the solid tomato pieces, stir all around with salt, and cook until starting to caramelize. The bottom of the pan should be brown, but not black.
Add the wine to deglaze the bottom of the pan, working everything up with a wooden spoon. Add the eggplant back in, then the water or stock, and finally the lentils, plus a big pinch of salt. Stir all around as the liquid comes to a boil. Lower heat to a simmer, and cook until the lentils are completely tender, about 30 - 40 minutes. You may need to add more water or stock if the lentils get too thick.
Towards the end of its cooking time, start seasoning with the Urfa chili and black pepper. Keep adding sprinklings of both until you really taste it. Don't be timid! This is what makes the lentils special.
Scoop into bowls and top with the sour cream and cilantro. Eat right away.