In a small bowl combine mayonnaise, Sriracha, lime juice and minced garlic. Stir until smooth and adjust heat by adding extra Sriracha to taste. Refrigerate until assembly.

Split the brioche buns and spread the cut sides lightly with softened unsalted butter.

Heat a skillet or griddle over medium heat. Toast the buttered cut sides of the buns, buttered-side down, until golden brown (about 1–2 minutes). Remove and keep warm.

Eggs & Seasoning

Whisk the 3 cage-free eggs in a bowl with the whole milk, salt and black pepper until blended and slightly frothy (about 20–30 seconds).

Heat a nonstick skillet over medium-low and add neutral oil to coat. Pour in the egg mixture and let sit undisturbed for 10–15 seconds.

Using a silicone spatula, gently push the set edges toward the center while tilting the pan to allow uncooked egg to flow underneath. Repeat slowly to create soft, slightly folded scrambled eggs. Cook until just set but still moist and slightly glossy — remove from heat about 20–30 seconds earlier than fully dry; carryover heat will finish them. Total cook time about 2–3 minutes.

Toppings

While eggs cook, warm the chopped kimchi in a small saucepan over low heat for 1–2 minutes to take the chill off and soften it slightly, then drain any excess liquid. This concentrates flavor and prevents sogginess in the sandwich.

Prepare nori: tear the sheet into strips or small pieces to distribute over the sandwich.

Slice the green onions, keeping whites and greens separated. Lightly toast sesame seeds in a dry skillet over low heat until fragrant if not already toasted, about 1 minute.

Assembly & Serve

Spread a generous layer (about 1 tbs) of the Sriracha aioli on the bottom half of each toasted brioche bun.

Divide the scrambled eggs evenly between the two buns, shaping them slightly so they sit neatly on the bun bottoms.

Top the eggs with about 2 tablespoons warm chopped kimchi per sandwich, then sprinkle furikake (about 1/2 tsp per sandwich) over the kimchi and eggs.

Add torn nori pieces and sprinkle toasted sesame seeds and sliced green onion whites over the top. Finish with the green parts of the scallion for color and mild bite.

Smear the top bun with a little extra Sriracha aioli if desired, close the sandwich, and serve immediately with optional pickles or extra Sriracha on the side.