Preheat the oven to 425°F. Peel about two-thirds of the skin from each eggplant by running a vegetable peeler the length of it, leaving alternate bands of skin and peeled areas (this just adds a bit of color and texture to the finished dish). Remove stems and cut the partially peeled eggplants into 3/4-inch cubes.
Put half of the cubed eggplant into a large mixing bowl and gradually drizzle in 1/3 cup olive oil, tossing to coat. Gradually sprinkle 1 teaspoon salt and a few generous grindings of black pepper, while tossing to evenly distribute the seasonings. Spread out the eggplant in one layer on a large metal baking sheet (lined with parchment or wax paper, if you like), keeping the pieces from crowding. Repeat the process with the remaining eggplant. Roast until just tender and golden-brown on the undersides, about 30 minutes, rotating the pans after 15 minutes to encourage even cooking.
While the eggplant roasts, dissolve the tomato paste in 1/4 cup water and set aside. Heat 3 tablespoons olive oil in a 10- to 12-inch skillet over medium-high heat. When the oil just begins to smoke, add the onion and celery and cook until the vegetables just begin coloring at the edges, but are still crisp, about 3 minutes, stirring regularly. Stir in the fennel and garlic and cook for 2 minutes. Reduce the heat to medium and cook until the fennel is tender but still a bit firm, 8 to 10 minutes, stirring occasionally (the vegetables should brown only slightly at the edges and each should retain its shape and some firmness). Stir in the dissolved tomato paste and 1 teaspoon salt and cook for 3 to 4 minutes, stirring regularly. Transfer the vegetable mixture to a large mixing bowl.
When the eggplant is tender, remove from the oven and let cool for at least 10 minutes. Meanwhile, put the orange zest, orange juice, vinegar, and sugar in a small saucepan. Bring to a simmer over medium heat, stirring to dissolve the sugar. Simmer until reduced in volume by one-third, 2 to 3 minutes. Remove from the heat.
Using a thin metal spatula, scrape up the eggplant on the pans to inspect the undersides of the pieces. Discarding any that have deeply burned (though some blackened bits are fine), put the roasted eggplant into the bowl with the vegetable mixture. Add the roasted red peppers, capers, pine nuts, and plumped raisins, folding gently with a large rubber spatula to combine (try not to mash the eggplant). Gradually drizzle in the warm orange-vinegar mixture while continuing to fold until everything is well combined. Add salt to taste and, if necessary, additional vinegar and orange juice to taste. The caponata should be pleasingly sweet and sour but not excessively sharp. Serve at room temperature or slightly cool.
Spoon about 1/2 cup caponata onto each of four serving plates and set aside. Salt and pepper the lamb generously on both sides. Heat the oil in a skillet large enough to hold the lamb chops (or use two skillets) over medium-high heat. When the oil is hot, add the lamb and cook until nicely browned on both sides and cooked to your liking, about 3 1/2 minutes per side for medium-rare. Transfer the lamb to plates with the caponata and serve.