Preheat your oven to 400°F and line a baking sheet with parchment paper.
Toss the halved Roma tomatoes and whole garlic cloves with half of the olive oil, sea salt, and black pepper, then roast for 25 minutes until the skins are blistered.
While the vegetables roast, poach the chicken breast in simmering water for 12-15 minutes until fully cooked, then shred it into small pieces using two forks.
In a large pot, heat the remaining olive oil over medium heat and sauté the diced yellow onion until it becomes soft and translucent.
Add the roasted tomatoes, garlic, tomato puree, and vegetable broth to the pot, bringing the mixture to a gentle boil before reducing to a simmer for 10 minutes.
Use an immersion blender to blend the soup until completely smooth, then stir in the freshly chopped basil.
Ladle the soup into a bowl, stir in the shredded chicken, and finish with a dollop of Greek yogurt for a creamy texture.