Brush away any loose dirt on the mushrooms. Cut into bite-sized pieces and set aside. Using scissors, cut off the top stem of the chile guajillos. Open the chiles and scrape out and discard the seeds.

Heat the broiler in your oven.

Meanwhile, heat the olive oil in a heavy 5 quart Dutch oven with a lid. Add the onion and sauté for 3 to 4 minutes until the onions are translucent. Add the mushroom pieces and sauté briefly, about 2 minutes. Do not allow the mushrooms to overcook or shrink too much. Remove from the heat.

Place the chile guajillos and garlic cloves in a metal baking pan and toast under the broiler in your oven for 60 to 90 seconds. Place the chiles and garlic in the container of a blender along with the water or vegetable stock. Purée well until smooth.

Pour the chile purée over the mushrooms and onions. Stir to combine well. Add the bundle of thyme.

Cover the Dutch oven and return to the heat. Allow to simmer for 25 minutes over a medium low heat.

Once the pozole is cooked, remove from the heat. Remove the bundle of thyme. Add the drained hominy and stir to combine well.

Serve the pozole hot and pass the garnishes of oregano and radishes. Best flavor is achieved when made 1 day in advance of serving.