Heat the olive oil in a large frying pan over medium heat. Add the onion, celery, carrot, garlic, chili, and thyme, and sauté for about 5 minutes until softened. Squeeze out the soaked dried porcini (reserve the soaking water) and stir into the pan. Add the fresh mushrooms and sauté for 1 minute or so. Increase the heat, add the white wine, and allow to evaporate.
Add the tomatoes, the reserved porcini soaking water, and the stock, and season with some salt and pepper. Bring to a boil, then lower the heat, partially cover with a lid, and cook gently for 45 minutes.
Just before the mushroom ragù is ready, bring a large saucepan of salted water to a boil and cook the pappardelle pasta until al dente, 2-3 minutes.
Drain the pasta and combine well with the ragù. Serve immediately with a sprinkling of grated Parmesan and some fresh thyme.