serve with a roasted pepper and eggplant spread, available at Middle Eastern markets
Whisk 2 tablespoons oil, sour cream, and horseradish in small bowl. Season to taste with salt and pepper.
Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Add onion and sauté until beginning to soften and brown, stirring often, about 8 minutes. Reduce heat to medium-low and cook until onions are very soft and deep golden brown, stirring often, about 20 minutes. Transfer to bowl. DO AHEAD Horseradish sauce and caramelized onion can be made 1 day ahead. Cover separately and chill.
Place rack on rimmed baking sheet. Place pork between 2 sheets of plastic wrap, spacing apart. Using flat side of meat tenderizer or mallet, pound to thickness of 1/4 inch. Place flour in 1 shallow bowl. Beat eggs in another shallow bowl. Place panko in third shallow bowl. Sprinkle pork with salt and pepper. Working with 1 pork chop at a time, dredge both sides in flour, shaking off excess; dip in eggs to coat. Transfer to panko and press to coat pork all over. Place on prepared rack. DO AHEAD Can be made 1 hour ahead. Let stand at room temperature.
Heat 2 tablespoons oil in heavy large skillet over medium-high heat. Add pork to skillet and cook until golden brown and cooked through, about 3 minutes per side, adding more oil by tablespoonfuls if needed. Transfer pork to paper towels.
Spoon 1 1/2 tablespoons ajvar onto each roll bottom; top each with 2 tablespoons caramelized onion. Place pork atop onion, then top with lettuce. Spoon 1 rounded tablespoon horseradish sauce onto cut side of each roll top. Place roll tops on sandwiches and serve.