Heat a 3-quart Dutch oven over medium heat. Add 2 tablespoons olive oil and the carrots, celery, onion and 1 teaspoon salt. Stir with a wooden spoon and cook until the vegetables begin to soften, about 4 minutes. Add the cherry tomatoes and chicken stock and stir to combine. Nestle the Parmesan rind and basil in the soup and bring to a simmer. Reduce the heat to maintain a gentle simmer and cook, stirring often to prevent the rind from sticking to the bottom of the pan, for about 25 minutes.
Remove the basil and Parmesan rind and discard. Stir in the mascarpone, the remaining tablespoon of olive oil and 1/2 teaspoon salt. Puree the soup until smooth with a stick blender. Serve topped with crumbled bacon.