Add the rice along with the ginger, garlic, and 10 cups of water to a large pot. Bring to a boil and reduce to a simmer and set a timer for 1 hour and 30 minutes.
In the meantime bring some additional water to a boil. Put the dried shiitake mushrooms in a heat proof bowl and cover with the boiling water. They tend to float, so I usually put another bowl on top of the mushrooms and water to help keep them submerged. Let them soak for 20 minutes or so until tender. Drain and discard the soaking water, then thinly slice the shiitakes.
Add the sliced shiitakes to the simmering pot of rice. It doesn't matter too much when you add the mushrooms, as long as they are in there with the rice for at least 20 minutes, but I always add them as soon as they are sliced.
Stir the pot every now and then as it simmers, especially as it gets closed to being finished so that it doesn't stick to the bottom of the pan. When the congee is done it will be a thick rice porridge. If you prefer a thinner congee, add water until desired consistency is reached.
Serve along with toppings of your choice. I like sliced green onions, chopped cilantro, sesame seeds, Sriracha, a few drops of toasted sesame oil, and soy sauce to taste.