Heat a large, heavy-based pan with a third of the oil and butter, add the onions and cook on high heat for 10 minutes, stirring, until translucent and brown. Tip the onions into a bowl. Add another third of the oil and butter to the pan and cook the button or chestnut mushrooms over medium-high heat for a minute without stirring (mushrooms become alarmingly watery without browning if they are stirred too much at this point). Stir briefly and then cook for another minute, then add to the bowl of onions. Fry the remaining mushrooms in the rest of the oil and butter using the same method, and again, add to the onions and other mushrooms in the bowl.
Tip the whole onion mushroom mixture back into the large, heavy-based pan, this time adding the vegetable stock, lots of salt and white pepper and simmer on high heat for about 7–8 minutes, until reduced by two thirds. Reduce the heat and stir in the crème fraîche and English mustard, cooking gently over a low heat for 7 minutes. Finally, add the Ouzo or Pernod, tarragon and parsley. Adjust the seasoning to taste.
Now start on the polenta. In a deep saucepan in which you can stir without splashing, heat the milk and salt until simmering but not yet boiling. Slowly add the polenta in a stream, stirring all the while with a wooden spoon, keeping the pan over medium-high heat. The polenta will take a while to thicken and will be a paler yellow colour than you would expect of firmer polenta. The biggest mistake you can make is to add more polenta for fear that your mixture is not thickening and you have added too little. Be patient. The mixture will thicken, and when it does, it will thicken fast. When you have it at a consistency that is just a little softer than you think you want it, remove it from the heat and stir through the butter and cheese. Season with the flaked sea salt and black pepper.
To serve, spoon a generous dollop of polenta into shallow bowls. The mixture will firm more as it cools. Make a little indentation in the middle of the polenta and spoon over the mushroom mixture. Garnish generously with micro leaves.