Mix together ground flax and water and set it aside to thicken for 10 minutes.
Mix together nondairy milk, apple cider vinegar, vegan oyster sauce, garlic powder, basil, and white pepper. Add the flax mixture once thickened, and then pour the marinade over the pieces of oyster mushrooms in a large zipper bag ensuring they are well submerged. Refrigerate for 15 to 20 minutes.
Meanwhile, mix together the breading ingredients and set aside.
You can combine the sandwich sauce ingredients together in a small dish in advance, or while the mushrooms are marinating and leave in the fridge until ready to assemble.
Heat oil to 365°F in a large iron skillet or heavy flat bottomed pan, or do this in a deep fryer because the mushrooms will splash oil with all their moisture! Oil should be heated up to the right temperature just as you're about to bread the oyster mushrooms.
Remove a few oyster mushroom pieces from the marinade and place directly in the breading coating evenly on all sides using your hands. Place each piece into the hot oil and fry for 2 to 3 minutes, flipping half way through.
Using a pair of tongs, place the fried pieces onto paper towel to absorb excess oil. Continue to bread the oyster mushrooms and fry in small batches.
To prepare the sandwiches, cut rolls in half and toast lightly if desired. Spread the remoulade on either side. Layer romaine lettuce, tomato slices, pickles, then fried oyster mushrooms. Serve immediately while the oyster mushrooms are still warm and enjoy!