Preheat your oven to 400°F and line a baking sheet with parchment paper.
Halve the Roma tomatoes and roughly chop the onion, then place them on the baking sheet with the whole garlic cloves.
Drizzle the vegetables with olive oil and sprinkle with sea salt and black pepper, tossing to coat evenly.
Roast the vegetables for 25-30 minutes until they are tender and slightly charred around the edges.
While the vegetables roast, poach the chicken breast in simmering water for 12-15 minutes until cooked through, then shred it using two forks.
Transfer the roasted tomatoes, onion, and garlic into a high-speed blender, ensuring you include any juices from the pan.
Add the chicken broth and fresh basil to the blender and process until the soup is completely smooth.
Pour the blended soup into a pot over low heat and stir in the Greek yogurt until fully incorporated and creamy.
Fold the shredded chicken into the soup, heat until warmed through, and serve immediately.