Prepare the Bulgur: In a medium saucepan, combine the bulgur wheat and water. Season with a pinch of salt. Bring to a boil over high heat. Once boiling, cover the saucepan, reduce the heat to low, and simmer for 10-12 minutes, or until the bulgur is tender and all the liquid has been absorbed. Remove from heat, let it sit covered for 5 minutes, then fluff with a fork. Transfer the cooked bulgur to a large serving bowl and allow it to cool completely.
Cook the Mushrooms: While the bulgur is cooling, heat a large skillet over medium heat. Add a tablespoon of olive oil and sauté the oyster mushrooms until they are soft, lightly golden, and their moisture has evaporated, about 5-7 minutes. Remove from heat and allow to cool. You can chop them more finely once cooled, if desired.
Prepare the Salad and Dressing: To the bowl with the cooled bulgur, add the finely chopped parsley, cooked mushrooms, diced tomatoes, and red onion. Toss everything together to combine.
Chill and Serve: Refrigerate the tabouleh for 30-60 minutes to allow the flavours to meld. Before serving, taste and adjust the seasoning with additional salt and pepper, if needed.