In a medium saucepan heat 3 tablespoons of the oil and, when hot, add the onion and garlic and cook until soft and fragrant, about 4 minutes. Add the tomatoes and their juices, olives, capers and caper juice, anchovies, crushed red pepper flakes, oregano, 2 tablespoons of the basil, and cook, stirring occasionally, until the sauce is very thick and flavorful, 30 to 40 minutes. Season with salt, to taste, and a pinch of sugar if the sauce seems too acidic. Cover and set aside.

Preheat the oven to broil and position oven rack about 4-inches from the broiler. Line 2 or 3 large baking sheets with parchment paper. Lightly brush the eggplant slices on both sides with the remaining olive oil and season lightly on both sides with salt and pepper. Place the eggplant slices on the baking sheets and broil until lightly golden on 1 side and the eggplant slices are pliable, 3 to 4 minutes. Repeat with remaining slices. Set aside.

Reduce the oven temperature to 350 degrees F.

Butter the inside of a 10-inch springform pan with the butter and coat the sides and the bottom with 6 tablespoons of the bread crumbs. Choose the nicest slices of eggplant and, working in a circular direction, line the bottom and sides of the springform, overlapping slices generously so that the eggplant slices resemble the spokes of a wheel. Set aside enough slices to cover the top, then cut the remaining eggplant slices into rough dice and transfer to a large mixing bowl, along with 1 3/4 cups of the reserved sauce, the cooked and drained bucatini, provolone, remaining 2 tablespoons of bread crumbs and the remaining fresh basil. Toss to combine and season, to taste, with salt and pepper. In a small bowl combine the egg and heavy cream, add this to the pasta mixture and toss again to thoroughly combine.

Turn the pasta mixture into the lined mold and arrange the reserved eggplant slices so that the top of the mold is completely covered. Press downward over the timbale to compress the filling. Bake, uncovered, for 45 minutes. Remove the timbale from the oven and run a thin paring knife around the sides of the springform pan to loosen the timbale. Let cool on a rack for 15 to 20 minutes before serving. While the timbale is resting, reheat the pasta sauce for serving. When ready to serve the timbale, loosen the sides of the springform pan and invert timbale onto a large serving platter. Using a sharp knife, slice into wedges for serving, with the warmed pasta sauce spooned over the top as desired.