Heat up half the olive oil in a large frying pan. Once hot, add half of the mushrooms and fry for a few minutes, or until just cooked; try not to move them much so you get golden-brown patches on their surface. Remove from the pan, and repeat with the rest of the mushrooms and oil. Off the heat, return all the mushrooms to the pan and add the garlic, tarragon, thyme, and some salt and pepper. Keep warm.
Bring the stock to the boil in a saucepan. Slowly stir in the polenta, then reduce the heat to the minimum and cook, stirring constantly with a wooden spoon. The polenta is ready when it leaves the sides of the pan but is still runny. If you are using instant polenta this shouldn’t take more than 5 minutes; with traditional polenta it could take up to 50 minutes (if it seems to dry out, add some more stock or water but just enough to keep it at a thick porridge consistency).
Preheat the grill to high. When the polenta is ready, stir in the Parmesan, butter, rosemary and half the parsley or chervil. Season with salt and pepper. Spread the polenta over a heatproof dish and top with the Taleggio. Place under the grill until the cheese bubbles. Remove, top with the mushrooms and their juices, and return to the grill for a minute to warm up. Serve hot, garnished with the remaining chervil or parsley.