Start with your dried shiitakes. Place them in a heatproof bowl and pouring almost boiling water over them. Let them sit until softened. Make sure the reserve the liquid to use as your mushroom broth later.
While the shiitakes are prepping, begin your polenta by bringing 5 cups of water to a boil, then slowly sprinkle in one cup of cornmeal while whisking continuously. Turn the heat down to low, and clap on a lid. You can let it simmer while you prep the sauce. It can stay on low for 20-40 minutes, giving it the occasional stir.
While that simmers, start your ragout by wiping down your criminology and oyster mushrooms and giving them a slice. Take your softened shiitakes out of the water and give them a gentle squeeze before slicing them, too. Then, taking extra care not to crowd your mushrooms, cook your assortment on a medium high heat in a large skillet with some olive oil. I had to cook mine in three rounds, just so that the mushrooms could brown nicely (if you threw them all in at once, their moisture would just cause them to simmer in their own juices). I used a total of 1 tsp of salt, but feel free to distribute that amongst the mushrooms as you cook them in rounds.
Next, saute the onion until soft and then add your mushrooms back into the pan all at once. Pour in the sherry to deglaze the pan and grab all that beautiful color from browning your mushrooms (use a wooden spoon to really scrap at the pan for all that cooked-on flavor).
Lastly, add your coconut milk and mushroom broth. Let the mixture simmer with the thymes, salt and pepper for about 5 minutes.
Returning to your awaiting polenta, stir in the plant-based milk, nutritional yeast (optional), salt and pepper. If you feel like it has become to thick, feel free to add a little water (about a 1/4 cup at a time).
Plate the polenta in a shallow bowl or plate, and top with the rich mushroom ragout. Garnish with a little chopped parsley or chopped chives, and serve hot.