Finely chop the mushrooms, onion, carrot and celery (a food processor makes this fast) and mince the garlic. Rinse the lentils.
Heat the oil in a large pot over medium heat. Add the chopped vegetables and cook, stirring, until soft and the mushroom liquid has evaporated, about 10 minutes.
Add the garlic and tomato paste and stir for 2 minutes until the paste darkens.
Add the lentils, crushed tomatoes, broth, Italian seasoning and salt. Bring to a boil, then lower the heat to low and simmer partly covered for 25 minutes, stirring now and then, until the lentils are tender.
Meanwhile, bring a large pot of salted water to a boil over high heat and cook the pasta for the time on the package, about 11 minutes. Save a mug of water and drain.
Toss the pasta with the sauce, the nutritional yeast and a splash of pasta water until glossy.