Place celery, carrots and onions in a food processor and pulse until finely chopped.: Close your eyes and picture the soft, green peppery scent of celery mingling with the sweet, oniony aromas as the pieces become uniform. This ensures even cooking and avoids large crunchy bits that break the sauce's texture. A common issue is over processing into a puree which can make the base too loose; pulse just until finely chopped but still slightly defined.
Heat 2 tbsp olive oil in a large pot over low to medium heat and sauté the onion mixture for 8 minutes or until softened.: The pan should hiss gently, and soon a sweet, caramel scent will rise as the onion , carrot , and celery soften. You want glossy, translucent vegetables, not brown bits, because slow sweating draws out sugars that balance the tomatoes. Stir occasionally to avoid scorching along the bottom, and resist turning the heat up to rush this step, which can create bitter flavors.
While the onions are cooking, place the mushrooms in the food processor and finely chop. Add to the onion mixture and sauté an additional 4 minutes.: As the chopped mushrooms hit the warm oil they'll release moisture, then begin to brown, producing a deep, roasted aroma and concentrated umami. The sound changes from sizzling to a soft bubbling as moisture evaporates. Avoid adding them while still wet from washing, which prolongs steaming; pat them dry first.
Add the salt, pepper, thyme, lentils, vegetable broth, tomato paste, balsamic vinegar and crushed tomatoes, bring to a boil, reduce to a simmer and cook covered over low heat for 45 minutes to 1 hour or until lentils are tender.: When everything goes in, the kitchen fills with a complex tomato and herb perfume. Bring to a vigorous boil briefly so the pot reaches even temperature, then lower to a gentle simmer where you will see small, steady bubbles. The lentils soak up flavors and swell, while the tomato paste integrates and deepens. Stir occasionally to prevent sticking, and check the seasoning halfway through. Over reducing can dry the sauce, so add more vegetable broth if it looks too tight.
While the sauce is simmering, cook the pasta according to package directions.: The water should roar when you add the spaghetti or pappardelle , and a pinch of salt will season the noodles through. Cook until the pasta is al dente, which means still slightly firm to the bite, because it will finish cooking when tossed with the hot sauce. Avoid overcooking into a soft texture, which will make the final dish mushy.
Remove the bay leaves and thyme stems from the sauce. Toss the pasta with the bolognese, sprinkle with parmesan and fresh basil if desired.: At this finish stage the sauce should smell rounded and rich, with a sweet tang from the balsamic vinegar and a savory depth from the mushrooms and lentils . Tossing the warm pasta with the sauce allows the noodles to soak up some liquid, marrying textures. Always fish out whole herb stems and bay leaves, since they are fibrous. If the sauce seems too loose, let it reduce a minute; if too thick, reserve some pasta water to loosen it gently while maintaining flavor.