Roughly chop the onion, carrot and celery and add to a food processor with the garlic, thyme and rosemary. Process the veggies until they are finely chopped.
Heat the olive oil in a large sauté pan over medium heat. Add the veggie mixture, salt, pepper and chili flakes. Sauté for 5 minutes, stirring consistently so the garlic doesn’t burn.
Roughly chop the cremini mushrooms and transfer to the food processor, along with the dried mushrooms. Process until they are finely chopped.
Add the mushrooms to the pan and sauté another 5 minutes, until they start to brown slightly.
Stir in the tomato paste to coat the veggies. Pour in the wine, mixing with a wooden spoon so it is well incorporated. Turn the heat to low and let simmer for 10 minutes. Cook the polenta in the meantime and serve the ragout over the polenta with fresh parsley for garnish.
In a small pot, bring the vegetable broth, salt, thyme, and rosemary to a boil.
Whisk in the polenta and set the heat to low. Let the polenta simmer for 5-10 minutes, stirring occasionally, until smooth yet still slightly runny (the polenta will firm up as it rests).
Stir in the Parmesan and serve the polenta with the ragout over the top.