Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Toss the cherry tomatoes, chopped yellow onion, and whole garlic cloves with olive oil, sea salt, and black pepper directly on the baking sheet.
Roast the vegetables for 20 to 25 minutes until the tomatoes have blistered and the onions are slightly charred and sweet.
While the vegetables roast, season the chicken breast with a pinch of salt and pepper and grill or pan-sear over medium heat until the internal temperature reaches 165°F.
Let the chicken rest for 5 minutes before slicing it into thin, bite-sized strips.
Transfer the roasted vegetables and any accumulated juices into a high-speed blender along with the vegetable broth and fresh basil.
Blend on high until the soup is completely smooth and reaches a velvety consistency.
Pour the soup into a bowl and stir in the Greek yogurt until fully incorporated and creamy.
Top the soup with the sliced grilled chicken and garnish with additional fresh basil leaves before serving.