Preheat your oven to 400°F and line a baking sheet with parchment paper.
Place the halved Roma tomatoes, sliced onion, and garlic cloves on the sheet, drizzle with olive oil, and roast for 25 minutes until caramelized.
While the vegetables roast, cook the chicken breast in a skillet or steamer until the internal temperature reaches 165°F, then shred it with two forks.
Transfer the roasted vegetables and any accumulated juices into a high-speed blender along with the bone broth and fresh basil.
Blend on high until the soup is completely smooth and velvety in texture.
Pour the soup into a medium saucepan, stir in the shredded chicken, and simmer over low heat for 5 minutes.
Remove from heat, whisk in the Greek yogurt until fully incorporated, and season with sea salt and black pepper before serving.