Put the onion, carrots, celery root, celery, and garlic in a food processor with 4 tablespoons of oil. Pulse until the vegetables are ground but not pureed.
Put 2 tablespoons of the oil in a large skillet over medium-high heat. Add the bread crumbs and cook until they’re crisp, dark, brown, and sizzling, 3 to 5 minutes.
Return the skillet to medium-high heat and add the remaining 2 tablespoons of oil. When it’s hot, add the vegetables and cook, stirring frequently, until the onion becomes translucent, 3 to 5 minutes. Add the tomato paste, lower the heat, and cook, stirring frequently, until the mixture darkens, 8 to 12 minutes. Add the tomatoes and sprinkle with salt and pepper. Bring to a boil, and then reduce the heat to a simmer. Cook, stirring occasionally until the sauce thickens, 15 to 20 minutes.
Bring a large pot of water to a boil. When the water boils, salt it and add the pasta. Stir occasionally, and start tasting after 5 minutes. When the pasta is tender but not mushy, drain the pasta, reserving 1 cup of the cooking water. Add the pasta to the sauce in the skillet, raise the heat to medium-high, and cook, stirring constantly until the sauce is steaming, 1 to 2 minutes. If the sauce gets too dry as it heats, add the reserved cooking water, a tablespoon at a time. Taste and adjust the seasoning. Garnish with the parsley and bread crumbs and serve.