Drizzle the olive oil into a large soup pot or braiser over medium heat. When the oil is shimmery, add the carrots, celery, and onions. Sprinkle the salt over the top and stir well. Drop the heat to low, and sweat the vegetables, stirring frequently, until the onions are translucent and the celery and carrots are beginning to soften, about 7 to 8 minutes. Add the garlic and stir. Cook until the garlic is fragrant, about 1 minute.
Stir in the tomatoes, chicken or vegetable stock, stems of parsley and basil, dried thyme, and bay leaf. Bring to a boil, put the lid on the pot, lower the heat and simmer for 20 minutes. At this point, you can transfer to a container and refrigerate the base for up to 3 days, or freeze for up to 3 months, or you can stir in the tortellini and cook just long enough for the pasta to become al dente. Remove and discard the bay leaf, and parsley and basil stems. Tear the additional fresh basil and parsley over the soup and stir in to distribute. Scoop the soup into serving bowls and grate cheese over the top just before serving.