1. In a large pot, heat the olive oil over medium heat. Add the onion and garlic and cook until tender, about 5 minutes. Stir in the bay leaves.
2. Add the tomatoes and vegetable broth. Stir in the brown sugar and fresh basil. Season with red pepper flakes, salt, and pepper, to taste. Simmer on low for 15 minutes.
3. Remove the bay leaves from the pot. Use an immersion blender to blend the soup (or blend the soup in a standing blender and return to the pot). Stir in the Greek yogurt until well combined. Stir in the orzo pasta. Serve warm.