Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Place the halved Roma tomatoes, peeled garlic cloves, and diced yellow onion on the baking sheet.
Drizzle the vegetables with olive oil and sprinkle evenly with sea salt and black pepper.
Roast for 25 to 30 minutes until the tomatoes are blistered and the onions have caramelized edges.
While the vegetables roast, poach the chicken breast in simmering water for 12 minutes, then shred it finely with two forks.
Transfer the roasted vegetables and all their juices into a high-speed blender along with the chicken bone broth and fresh basil.
Blend on high speed until the mixture is completely smooth and reaches a velvety consistency.
Pour the soup into a medium saucepan over medium-low heat, then stir in the shredded chicken and Greek yogurt.
Whisk gently until the yogurt is fully incorporated and the soup is heated through.
Ladle the soup into a bowl and finish with a garnish of freshly grated parmesan cheese.