Coat the bottom of a large pot with 1/4 cup of olive oil. Place the pot over medium heat. Once the oil is hot, add the mushrooms. Cook for about 10 minutes, flipping occasionally with a spatula, until the mushrooms have reduced by about half in size and begun to release their juices. Transfer the mushrooms to a plate.
Add the remaining tablespoon of oil to the pot. Once the oil is hot, add the onion, carrots and celery. Sauté until the veggies have softened, about 10 minutes. Add the garlic and sauté until very fragrant, about 1 minute more.
Return the mushrooms to the pot, and stir in the wine. Bring it to a simmer and allow to cook until reduced by about half, about 4 minutes.
Stir in the tomatoes, milk, soy sauce, thyme, basil, oregano, fennel, red pepper flakes, and liquid smoke. Bring everything back up to a simmer and allow to cook, uncovered, until the sauce thickens up and the veggies are fully cooked, about 20 minutes, stirring occasionally.
While the sauce simmers, bring a large pot of water to a boil. Add the pasta and cook it according to the package directions. Drain the pasta into a colander, return it to the pot, and toss it with a dash of olive oil to prevent sticking.
Once the sauce has finished simmering, remove it from heat and season with salt and pepper to taste. Pour the sauce over the pasta and toss to mix everything up. Divide onto plates and serve.