Before you start, preheat oven to 220°C (or 200°C fan bake).
Prep potatoes and carrot. Spread out in a single layer on 1-2 lined oven trays and toss with oil and white sesame seeds. Season with salt and pepper and bake for 25-30 minutes, until tender and golden. Turn once during cooking.
Pat fish dry and remove any remaining scales or bones. Cut into fingers and season with salt. Add fish to a large bowl along with flour and toss to coat. Add egg to same bowl, split the yolk and toss to coat fish. Place breadcrumbs and black sesame seeds in another bowl and mix to combine. Place fish into crumbs, turn to coat each piece well and place on a plate/tray. Keep breadcrumbs plain for fussy little foodies.
Heat oil in a large fry-pan on medium heat. Cook fish in batches for about 2-3 minutes each side or until cooked through and golden. Add more oil between batches, if needed.
Cut rolls in half lengthways, leaving a hinge. Butter rolls, place on oven tray and cook below potatoes for about 4 minutes, until warmed through.
To finish, prep lettuce and cucumber.
Serve rolls filled with fish, lettuce, cucumber and mayo. Serve chips on the side.