Peel the carrots, parsnips, beet, onion, and celery root, if using, and remove the seeds from the bell peppers and jalapeño. Roughly chop all the vegetables to fit into the feeding tube of a food processor with a shredding attachment. Shred all the vegetables and transfer the mixture to a large, heavy-bottomed soup pot.
Add the oil to the pot and season to taste with salt and pepper. Turn the heat to medium and let the vegetable juices release and start simmering, then reduce the heat to low, cover the pot, and let the vegetables cook gently in their juices for 30 minutes, until all the juices are released and the vegetables are soft.
Meanwhile, change the food processor attachment to a slicer. Roughly chop the cabbage to fit into the food processor's feeding tube, and slice it using the attachment. Alternatively, thinly slice the cabbage by hand. Transfer the cabbage to a large bowl and cover it with cold water; set aside.
After the shredded vegetables have cooked for 30 minutes, place the potatoes on top and pour in enough water to cover the potatoes completely. Increase the heat to medium, bring the liquid to a boil, then reduce the heat to a simmer and cook, partially covered, for about 10 minutes, until the potatoes are soft.
Meanwhile, bring a kettle or medium saucepan of water to a boil. Drain the cabbage and add it to the pot with the potatoes and shredded vegetables. Pour the boiling water over the cabbage, filling the pot but leaving some room for the tomatoes. Add a few big pinches of salt. Simmer for 15 to 20 minutes or until the cabbage is soft, then add the crushed tomatoes and bring the soup back to a boil over medium heat. Taste for salt and adjust if needed. As soon as the soup comes to a boil, remove the pot from the heat and stir in the garlic and herbs.
For best results, let the borscht come to room temperature and then refrigerate it overnight so it can develop fully in flavor. When you're ready to serve it, reheat the borscht on the stove. Serve with sour cream and more chopped dill and parsley, if desired.