Heat the olive oil in a large pan over medium heat. Add the chopped onion and garlic, and sauté until translucent, about 2-3 minutes.
Add the sliced mushrooms, carrots, and celery to the pan. Cook, stirring occasionally, until the vegetables have softened and the mushrooms have released their liquid, about 5-7 minutes.
Pour in the red wine and vegetable broth. Stir well and bring the mixture to a simmer.
Add the crushed tomatoes, dried thyme, dried oregano, dried basil, bay leaves, salt, and pepper. Stir to combine.
Reduce the heat to low, cover the pan, and let the ragu simmer for about 20-30 minutes, stirring occasionally. The sauce should thicken and the flavors meld together.
While the ragu is simmering, cook the tagliatelle pasta according to the package instructions until al dente. Drain and set aside.
Once the ragu has thickened and the vegetables are tender, taste and adjust the seasoning as needed. Remove and discard the bay leaves.
Serve the mushroom ragu over the cooked tagliatelle pasta. Garnish with fresh basil leaves and vegan Parmesan cheese, if desired.Enjoy your vegan mushroom ragu on tagliatelle!