Preheat the oven to 200 degrees F (95 degrees C). Line a baking sheet with parchment paper.
Place cherry tomatoes on the prepared baking sheet, cut side up; sprinkle with sugar and oregano.
Bake in the preheated oven until completely wilted, about 1 hour.
Meanwhile combine celery, carrot, onion, peppercorns, and salt in a saucepan. Add enough water to fill the saucepan halfway. Cover and bring to a boil for 10 minutes. Add shrimp and poach for 5 minutes. Drain, peel, and chop shrimp.
Cut buffalo mozzarella into cubes; place in a colander or sieve to drain off excess water.
Place bread in the bowl of a food processor and pulse to make breadcrumbs. Heat 1 teaspoon olive oil in a pan over medium heat. Add breadcrumbs and cook until crispy and golden in color, about 3 minutes.
Mix the buffalo mozzarella cubes with cooked shrimp in a large bowl. Add chopped black olives and season to taste with olive oil, salt, and pepper. Arrange on a serving plate and top with caramelized tomatoes and toasted breadcrumbs. Drizzle with some more olive oil and garnish with basil leaves.