Remove the brown root block and divide the remaining mushrooms into small, flat pieces about 1 inch long and ½ inch wide at the base. Favor narrow fans with thoroughly dried stems, since dense clusters hold moisture in their centers.
Whisk the flour, cornstarch, salt, paprika, garlic powder, and pepper in a long, shallow container, then incorporate the cold water. The finished mixture should flow easily and show no dry pockets or lumps.
Warm the vegetable oil over medium heat in a pan containing at least 1.5 inches of oil. Small bubbles around an inserted toothpick tip indicate readiness, while a frying thermometer gives a clearer check of the 350°F target.
Turn each mushroom fan through the batter with tongs to coat both faces and the base, then lift it by the base to drain the excess. A thin film should remain on the stems rather than a thick blanket that glues them together.
Lower the coated fans carefully into the oil in uncrowded batches, cook for 1 minute, turn with tongs, cook for another minute or until golden brown, and lift onto the paper-towel-lined plate. Immediate bubbling and spreading strands indicate that frying is progressing, while a quiet pan means the oil needs more heat before the next piece.
Let the cooked mushrooms rest for 1 minute, then add any desired optional flaky salt, chives or scallions, and lemon juice before serving with the aioli. The coating should feel crisp and the mushrooms should still be warm.
During frying, stir the mayonnaise, Thai red chili paste, lemon or lime juice, and garlic together in a small bowl, adjusting with the optional salt or water if desired. The dip should look creamy and evenly blended, with heat and acidity balanced to your taste.