For the soup: In a medium saucepan, heat the olive oil over medium-high heat. Add the carrots, shallots, 1 teaspoon salt and 1/4 teaspoon pepper. Cook, stirring frequently, until the carrots are softened, 6 to 8 minutes. Add the chicken broth, orange juice, basil, maple syrup, tomato paste and the tomatoes (with juice). Bring the mixture to a boil, then reduce the heat and simmer, uncovered, for 15 minutes.
Using an immersion blender or food processor, puree the soup until smooth. Cool the soup to room temperature until ready to serve, about 1 hour. Season the soup with salt and pepper.
For the yogurt topping: In a small bowl, whisk together the yogurt, maple syrup and orange zest until smooth.
Ladle the soup into chilled bowls and top with a dollop of the yogurt mixture.
When blending hot liquids: Remove liquid from the heat and allow to cool for at least 5 minutes. Transfer liquid to a blender or food processor and fill it no more than halfway. If using a blender, release one corner of the lid. This prevents the vacuum effect that creates heat explosions. Place a towel over the top of the machine, pulse a few times then process on high speed until smooth.