Bring a large pot of salted water to the boil. Add the rice and lower the heat. Simmer for 10 minutes, then drain the rice. Place the rice in a bowl and drizzle with 1 tablespoon olive oil. Stir in 50 grams of grated cheese. Set aside.
Place the remaining olive oil in a large sauté pan over medium heat. Add the garlic and cook for a minute or two, then add the onions, peppers and eggplant. Cook over medium-high heat, stirring, for about 5 minutes. Then lower the heat to low, cover and stew for 10 minutes.
Remove the lid and add the tomatoes. Stir well, then cover again and cook for an additional 10 minutes.
Remove the lid, raise the heat to medium-high, add the capers, olives, red pepper flakes and basil leaves. Stir well and cook for a few minutes. Taste and adjust for seasoning.
Preheat the oven to 350 F/180 C. Oil a baking dish.
Place half the rice in the dish evenly. Distribute half the vegetable mixture over the rice evenly. Top with half of the remaining grated cheese. Repeat with the remaining rice, vegetables and cheese. Place the dish in the oven and bake for 25 minutes, until the top is a deep golden brown. Remove from the oven and let cool for 5 minutes before serving.