Preheat the oven to 350 degrees F.
In a medium cast-iron pan or braiser, bring the tomatoes and sauce, olives, salami and olive oil to a simmer over medium-high heat. Season with pepper and salt if necessary (the salami and the olives can be salty).
Arrange the mozzarella on top, make 4 wells and crack an egg into each. Season the eggs with salt and pepper. Sprinkle the basil on top and drizzle with more olive oil. Transfer the pan to the oven and bake until the eggs are set but still runny, about 20 minutes.
Toast the bread in a toaster and then rub with the garlic. Drizzle with olive oil, sprinkle with grated Pecorino and serve with the baked eggs.