Preheat your oven to 350°F (175°C) and generously butter a 9x13-inch casserole dish. Cut the bread into 1-inch cubes and spread them in an even layer in the prepared dish. In a large mixing bowl, whisk together the eggs, milk, salt, black pepper, and dried oregano until well combined. Dice the tomatoes into small chunks and slice the mozzarella into thin pieces. Mince the garlic cloves finely and tear the fresh basil leaves into smaller pieces. Layer half of the tomatoes, mozzarella, garlic, and basil over the bread cubes. Drizzle with olive oil. Pour half of the egg mixture evenly over the layers, pressing down gently to help the bread absorb the liquid. Add the remaining bread cubes if needed, then top with the rest of the tomatoes, mozzarella, garlic, and basil. Pour the remaining egg mixture over everything, again pressing gently to ensure even distribution. Sprinkle the grated Parmesan cheese over the top. Cover the dish with aluminum foil and let it rest for 15 minutes to allow the bread to soak up the custard. Bake covered for 30 minutes, then remove the foil and continue baking for another 15 minutes until the top is golden brown and the center is set. Remove from the oven and let stand for 5-10 minutes before cutting into squares and serving warm.