Heat ¼ cup of the olive oil in a large pot over medium heat. Add the mushrooms and cook for about 10 minutes, stirring occasionally, until they have reduced by about half and released their juices. Transfer them to a plate.
Add the remaining tablespoon of oil to the pot. Add the onion, carrots, and celery and sauté for about 10 minutes, until softened. Add the garlic and cook for 1 minute more, until fragrant.
Return the mushrooms to the pot and stir in the wine. Bring to a simmer and cook for about 4 minutes, until reduced by about half.
Stir in the tomatoes, milk, soy sauce, thyme, basil, oregano, fennel, red pepper flakes, and liquid smoke. Bring back to a simmer and cook, uncovered, for about 20 minutes, stirring occasionally, until the sauce has thickened and the vegetables are tender.
While the sauce simmers, cook the pasta according to the package directions. Drain it and return it to the pot.
Season the sauce with salt and pepper. Pour it over the pasta, toss to combine, and serve.
Notes
Almost any fresh mushrooms will work here. A mix of white button, cremini, shiitake, and oyster mushrooms gives the best flavor and texture.