Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Halve the Roma tomatoes and peel the onion, cutting it into thick wedges.
Place the tomatoes, onion wedges, and whole garlic cloves onto the baking sheet.
Drizzle the vegetables with olive oil and season evenly with sea salt, black pepper, and dried oregano.
Roast the vegetables for 30 to 35 minutes until they are soft and slightly charred around the edges.
While the vegetables are roasting, cook the chicken breast in a skillet or poach it in water until it reaches an internal temperature of 165°F, then shred it with two forks.
Transfer the roasted tomatoes, onions, and garlic (including any juices from the pan) into a high-speed blender.
Add the chicken bone broth and fresh basil leaves to the blender and process on high until the mixture is completely smooth and velvety.
Pour the blended soup into a medium pot over low heat, then stir in the shredded chicken and plain Greek yogurt.
Gently stir the soup until it is heated through and the yogurt is fully incorporated, then serve immediately.