Preheat the oven to 375 degrees F.
Add the eggplant to a baking sheet. Drizzle with 1/4 cup olive oil and sprinkle with salt and pepper. Roast for 20 minutes, until soft and tender.
Meanwhile, add 2 tablespoons olive oil to a saute pan over medium-high heat. Once hot, add the onion and garlic, and saute until tender, about 5 minutes; add the red pepper flakes. Stir in the tomatoes and cook until soft and beginning to break down, about 4 minutes. Stir in the roasted eggplant and the green olives and cook until everything is melded together. (You do not want the topping too saucy.) Turn off the heat and stir in the basil.
Toast the bread in the oven or on the grill (or if you are lucky enough to own one, on an Italian stovetop toaster).
To serve, add a nice-size dollop of the eggplant mixture to the warm bread and drizzle with olive oil. Garnish with shaved Pecorino and torn basil.