Layer eggplant slices in a bowl, sprinkling salt onto each layer. Set aside for 30 minutes. Spread a layer of paper towel on a work surface; drain eggplant slices on paper towels.
Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Mix diced tomatoes, tomato sauce, artichoke hearts, and roasted red peppers in a bowl.
Heat a skillet over medium-low heat; toast pine nuts, stirring occasionally, in the hot skillet until fragrant and lightly browned, 3 to 5 minutes. Stir toasted pine nuts, garlic, parsley, basil, oregano, and black pepper into tomato mixture using a fork.
Spread a layer of eggplant in the bottom of the prepared baking dish; spoon 1/3 the tomato mixture atop eggplant layer. Sprinkle 1/3 the red onion, 1/3 the mozzarella, and 1/3 the Pecorino-Romano cheese over tomato layer. Repeat layering until all ingredients are used.
Bake in the preheated oven until cheese is melted and golden brown, about 40 minutes.