Prep the vegetables: Dice the onion, celery, and carrots into small, even pieces. Smash and peel the garlic cloves. Chop the green beans and zucchini. Drain and rinse the beans.
Heat the olive oil in a large pot or Dutch oven over medium heat. Add the diced onion, celery, and carrots with a big pinch of salt. Cook, stirring, until soft and starting to go golden, 6-8 minutes. Add the smashed garlic cloves for the last minute.
Push the veggies to the sides of the pot. Add the tomato paste to the empty spot in the center and let it sizzle and darken for 1-2 minutes until it turns a deep rusty brick color, then stir it into the veggies. This is the non-negotiable depth step.
Pour in the can of whole tomatoes, crushing them with your hands as you go. Add the broth and the parmesan rind if using. Bring to a boil, then lower to a simmer. Let it bubble gently for 15 minutes.
Stir in the drained cannellini beans, chopped green beans, and diced zucchini. Simmer for 10 minutes, until the zucchini is tender.
Meanwhile, cook the pasta in a separate pot of salted boiling water until just shy of al dente (still a tiny white dot in the center). Drain and toss with a little olive oil. Why separately: so it doesn't soak up all your broth and turn into a mushy mess the next day.
Stir the cooked pasta into the soup. Taste for salt and add a big squeeze of lemon or a splash of red wine vinegar. Ladle into bowls, making sure to get a good mix of broth, beans, and veggies. Swirl with olive oil, shower with parmesan and fresh basil. Serve immediately.