Pickle the carrots. Dissolve salt and sugar in the warm water, then add rice vinegar. Add carrots and garlic and stir through; let stand for at least 1 hour - carrot should be a bit tangy - but best to make it a day before. These will last for up to a week in the refrigerator.
Prepare the eggplant. Cut eggplant into circles, about 0.5-0.7cm thick, and then cut those in half circles. Layer on a plate or a board and sprinkle lightly with salt to draw out some of the moisture. This helps to reduce the amount of oil needed to fry the eggplant (note, you will still need a lot!).
Prepare aromatics. While eggplant is doing its thing, dice and mince garlic, ginger and lemongrass and set aside. You can also prepare some of the other ingredients, although I do that while the eggplant is cooking.
Cook eggplant. Heat a thin layer of olive oil (about 5 tablespoons) in a large frying pan over medium to high heat. Add the eggplant slices (in batches or use two frying pans) and pan-fry for 2-3 minutes until golden brown. You may need to drizzle extra olive oil as the eggplant will absorb what was in the pan instantly. Turn over and cook for about 2 minutes on the opposite side. You may need a little extra oil but not as much.
Remove pre-cooked eggplant to a cutting board. Repeat with the remaining eggplant until it's all cooked.
Cook the aromatics. Add lemongrass, garlic and ginger to the same frying pan with a splash of olive oil. Cook for a minute, stirring a few times until it starts to get golden. In the meantime, roughly cut the eggplant.
Finish the eggplant. Add the cut-up eggplant, sprinkle with about 1/2 teaspoon of white pepper and drizzle 2 tablespoons of soy sauce over the top. Cook for about 2 minutes, stirring a few times. Remove eggplant to a bowl and set aside.
Prepare the chili. Chop the chili and mix with a little rice wine vinegar in a bowl, set aside.
Make the rolls. Split rolls down the centre and spread apart.
Spread 1.5 tablespoons of mayo on one side and arrange the iceberg lettuce on the other. Layer cucumber slices and pickled carrots over the mayo and spread about 1/4 cup of the eggplant on top of the lettuce (or as much as you like).
Sprinkle with chilli, plenty of coriander and green onions. Finish with a tablespoon of the fried shallots for texture. You can drizzle some of the pickling brine from carrots over the top.
Close the roll and bite in! You can cut it in halves for easier consumption.