Preheat your oven to 400°F and line a rimmed baking sheet with parchment paper.
Halve the plum tomatoes and place them on the baking sheet with the peeled garlic cloves, tossing with olive oil, sea salt, and black pepper.
Roast for 25-30 minutes until the tomatoes are soft and slightly charred around the edges.
While tomatoes roast, sauté the diced yellow onion in a medium pot over medium heat until translucent, about 5 minutes.
Transfer the roasted tomatoes, garlic, and any pan juices into the pot and pour in the vegetable broth.
Bring the mixture to a gentle simmer for 10 minutes to let the flavors meld, then stir in the fresh basil leaves.
Use an immersion blender to process the soup directly in the pot until it reaches a completely smooth and velvety consistency.
Stir in the shredded chicken breast and Greek yogurt, stirring over low heat until the soup is creamy and warmed through.
Ladle the soup into a bowl and garnish with the freshly grated parmesan cheese.