Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Halve the Roma tomatoes and place them on the baking sheet with the peeled garlic cloves.
Drizzle the tomatoes and garlic with half of the olive oil and season with the sea salt and black pepper.
Roast for 25 to 30 minutes until the tomatoes are soft 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 using two forks.
In a medium pot, sauté the diced yellow onion in the remaining olive oil over medium heat until translucent and fragrant.
Add the roasted tomatoes, garlic, and chicken broth to the pot and simmer gently for 10 minutes to meld the flavors.
Use an immersion blender to puree the soup directly in the pot until it reaches a smooth, velvety consistency.
Stir in the shredded chicken and Greek yogurt, heating through for 2 minutes without letting the soup reach a boil.
Divide into bowls and garnish with freshly chopped basil before serving.