Warm the olive oil in a large, wide pan over medium heat.
Add the finely chopped yellow onion and cook for 4–5 minutes, stirring often, until it softens and turns slightly translucent.
Stir in the minced garlic and cook for about 30 seconds, just until fragrant, making sure it does not brown.
Add the finely diced carrot and celery to the pan and cook for 4–5 minutes, stirring occasionally, until the vegetables begin to soften.
Add the finely chopped mixed mushrooms to the pan, stir well, and cook for 8–10 minutes, allowing their moisture to release and then evaporate, until the mushrooms start to brown lightly.
Stir in the tomato paste and cook for 1–2 minutes, stirring, to lightly caramelize it and deepen the flavor.
Pour in the dry red wine, scraping the bottom of the pan with a spoon to release any browned bits, and let it simmer for 2–3 minutes until slightly reduced.
Add the canned crushed tomatoes, vegetable broth, dried thyme, dried oregano, salt, black pepper, and soy sauce, then stir until everything is well combined.
Bring the mixture to a gentle simmer, then reduce the heat to low and cook uncovered for 20–25 minutes, stirring occasionally, until the mushroom ragu has thickened to a rich, spoonable consistency.
Taste the mushroom ragu and adjust the seasoning with a little more salt and black pepper if needed.
Stir in the chopped fresh parsley just before serving, and serve the mushroom ragu warm.