Bring a pot of water to a boil. Crack an egg in a small bowl (this makes it easier to drop in the water). When water is boiling, use a spoon to create a whirlpool. Carefully, drop the egg into the water and keep swirling the water as the egg turns white. Cook for about 2-3 min or until egg is white and strong enough to hold its form. I do 1 egg per toast, so repeat with however many toasts you are making.
Using 3 bowls, add panko, flour and 1 whisked egg to each. Coat egg in flour, then egg, then panko breadcrumbs. Add fry oil to a pan, about an inch up the side. Heat oil until it gets to 375. Add egg and cook for about 2 min per side or until egg is nicely golden brown. Careful to not overcook if you want to keep a slightly runny egg.
Drizzle scallions with olive oil and add to a grill on high heat. Alternatively, you could add to a hot pan. Cook until outside is charred and the scallions are tender. Season with salt and pepper.
Slice scallions into bite sized pieces and add to a bowl. Season with olive oil, salt, pepper, red pepper flakes, lime juice and a drizzle of vinegar. Season to taste.
Coat bread in olive oil and cook for 2-3 min per side. Add mascarpone, charred scallions and fried egg. Drizzle a little more lime juice over top and enjoy!