Heat the olive oil in a medium saucepan over medium heat until it shimmers but does not smoke. Add the onion, porcini mushrooms, and a pinch of salt, then cook until the onion is softened and starting to brown, about 5 to 7 minutes.

Increase the heat to medium-high and stir in the cremini mushrooms. Cook, stirring occasionally, until the mushrooms have browned and their liquid has evaporated, about 8 minutes. Add the garlic and cook until fragrant.

Stir in the bulgur and cook until the grains are lightly toasted and fragrant. Pour in the broth, water, and soy sauce, then bring the mixture to a boil. Reduce the heat to low, cover, and simmer until the liquid is fully absorbed and the grains are tender, about 12 to 15 minutes.

Remove the saucepan from the heat and take off the lid. Place a clean, folded kitchen towel over the top of the pot and replace the lid firmly. Let the pilaf stand for 10 minutes—the towel will catch the excess steam and prevent the grains from becoming soggy.

Remove the lid and towel, then fluff the bulgur with a fork. Stir in the parsley, season with salt and pepper to taste, and serve hot.