To prepare the mushrooms, mix together the milk and vinegar and allow to thicken to a buttermilk consistency.
In another bowl, mix together the breading.
Heat the oil in a heavy-bottomed pot to a temperature of 365°F to 375°F on a deep-frying thermometer. The oil should be heated to the right temperature just as you’re about to bread the mushrooms.
Pull the mushrooms apart into desired size. Dredge the mushrooms in the milk and flour breading, then drop into the hot oil and fry for 2 to 3 minutes.
Place fried mushrooms on paper towels to absorb excess oil. Continue to bread the mushrooms and fry in small batches.
To assemble the sandwiches, cut the rolls in half and toast, if desired. Spread some Tabasco Aioli on the inside of each roll. Layer the romaine lettuce, tomato slices, and fried mushrooms on one half of each roll. Add more aioli, if desired. Serve immediately while the oyster mushrooms are still warm.