Arrange a rack in the middle of the oven and heat to 350°F. Place the eggplant directly on the oven rack and bake until very tender, 1 to 1 1/2 hours. Cool the eggplant while preparing the rest of the sauce.
Meanwhile, heat a large frying pan over medium-high heat until hot. Add the mushrooms and brown, stirring occasionally, until they’ve shrunk by about half, 8 to 10 minutes. Set the pan aside.
Soffritto: Heat the oil in a large Dutch oven over medium heat until shimmering. Add the onion, celery, and carrots, and season with 1/4 teaspoon of the salt. Cook, stirring frequently, until the vegetables are softened, 10 to 12 minutes.
Pour the wine onto the soffrito mixture and stir to combine. Reduce the wine by half, stirring occasionally, 5 to 7 minutes.
Add the garlic, basil, oregano, thyme, and tomato paste and cook until thickened and fragrant, about 5 minutes.
Peel and coarsely chop the cooled eggplant. Add the eggplant, reserved mushrooms, crushed tomatoes, and 1/2 teaspoon of the salt to the soffritto mixture and stir until thoroughly combined.
Reduce the heat to low and cover. Simmer, stirring occasionally to prevent scorching, until the sauce is quite thick, at least 1 hour.
Bring a large pot of salted water to a boil over medium heat. Add the pasta and cook to al dente.
Use a slotted spoon to transfer the pasta from the cooking water to the sauce. Don’t worry about any pasta-cooking water that might fall into the sauce as well — this will help season and thin the sauce. Cook the pasta for an additional 2 minutes in the sauce.
Serve with additional fresh chopped herbs and nutritional yeast or Parmesan cheese, as desired.