Preheat your oven to 400°F (200°C).
Halve the Roma tomatoes and the yellow onion, then place them on a large baking sheet along with the peeled garlic cloves.
Drizzle the vegetables with olive oil and sprinkle with sea salt and black pepper.
Roast the vegetables for 25 to 30 minutes until they are tender and have developed a slight char.
While the vegetables roast, poach or pan-sear the chicken breast until the internal temperature reaches 165°F, then shred it finely 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 vegetable broth and fresh basil to the blender and process until the mixture is completely smooth and velvety.
Pour the soup into a serving bowl, stir in the Greek yogurt until well incorporated, and top with the warm shredded chicken.