If using freshly foraged chanterelles, remove dirt by gently rinsing them.
Set a skillet on medium heat and melt the butter. Dice the onion and add it to the butter. Add the dried thyme and sauté until the onion is soft, about 5 minutes.
Add the chanterelles and increase the heat. The mushrooms will release quite some water, cook them on high heat until all the water has been evaporated and the chanterelles are wilted.
When the water has evaporated, stir in the balsamico and the salt and remove from the heat.
Add the cream and stir in.
As the mushrooms are cooking, set a pot of water on high heat, add salt and olive oil and bring to a boil.
When the water boils, reduce the heat to medium-high and pour in the polenta in a slow stream, mixing with a hand whisk as you pour the cornmeal.
Cook the polenta according to package instructions. Instant polenta should thicken after about 6 minutes of cooking.
Remove the polenta from the heat. Lightly warm the milk and stir it into the polenta.
Add half of the polenta to an oven-safe dish. Dice the cheeses and add place 3/4 of them over the polenta. Cover with the remaining polenta and place last bits of cheese on top.
Melt the butter and pour the butter on top of the polenta.
Bake for 10 minutes at 200°C (390°F).
Serve the polenta concia with chanterelle sauce on the side, preferably in a bowl.