Pre-heat the grill in the oven to 450ºF with rack in top position.
Line a baking tray with parchment paper.
Clean and trim the button mushrooms and cut them in slices.
Clean the big cap mushrooms with a wet cloth and a brush. Brush a little olive oil on the top of the caps and grill them for 6 minutes.
Chop the parsley and garlic very finely. Remove the leaves of the thyme.
In a sautée pan, over moderate high heat warm the olive oil. Sautée the button mushroom slices until golden. Add the thyme leaves, garlic and parsley and cook for a further 2 minutes. Season with salt and pepper.
Cut the gorgonzola in small pieces.
For the Polenta: In a heavy pan bring water and salt to a boil. Pour the cornmeal in a steady stream and whisk. Lower heat to low and cook the polenta so that it barely boils, whisking constantly. When it starts to thicken, use a wooden spoon and continue cooking for 45 minutes, stirring every 5 minutes until the polenta creates a crust in the pan and pulls away from the sides. If using pre-cooked polenta follow the instructions in the package.
Finish off the polenta - Add the butter to the polenta and stir very well until butter is melted and incorporated and polenta is creamy.
In an oven proof dish (individual or one big one) spread a layer of polenta, top with the big cap grilled mushroom bottom up, fill the inside of the cap with polenta, add sautéed button mushrooms and finish with 1 tablespoon of gorgonzola on top of the mushrooms and another tablespoon of gorgonzola over the first layer of polenta.
Lower the oven rack to middle position and grill the polenta/mushrooms/gorgonzola until golden brown.