Preheat your oven to 400°F (200°C).
On a large baking sheet, toss the halved Roma tomatoes, chopped onion, and peeled garlic cloves with 0.5 tablespoons of olive oil, sea salt, and black pepper.
Roast the vegetables for 25-30 minutes until the tomatoes are blistered and slightly charred around the edges.
While the vegetables roast, poach the chicken breast in simmering water for 12-15 minutes until fully cooked, then remove and shred with two forks.
Transfer the roasted vegetables and all their juices into a high-speed blender; add the chicken bone broth and fresh basil leaves.
Blend on high until the soup reaches a velvety, smooth consistency.
Pour the blended soup into a medium pot, stir in the shredded chicken, and simmer over low heat for 5 minutes to meld the flavors.
Brush the sourdough slice with the remaining 0.5 tablespoons of olive oil, sprinkle with Parmesan cheese, and toast in the oven or a toaster oven until the cheese is bubbly and golden.
Ladle the hot soup into a bowl and serve immediately with the warm Parmesan crostini.