Bring a pot of water to a boil. Gently place the eggs in the pot, cover, and cook for six and a half minutes. Once cooked, immediately take the pot off the stove and place under cold running water. Move the contents to a bowl with ice cubes and water, let rest for 10 minutes. Carefully remove the shells from the eggs.

Mix the soy sauce, sugar, mirin, sake, honey, and miso in a sealable bag. Add the eggs. Seal and make sure the eggs are fully covered. Place in the refrigerator and marinate for at least 24 hours. Can be stored in the refrigerator for up to three days. To serve on the burger, make sure to cut into slices.

Preheat an oven to 325°Bring a pot of water to a boil. Add the pork and simmer for 5 minutes.

Remove the pork belly from the water. In a dutch oven, mix the sugar and water over medium-high heat. Whisk until the sugar has dissolved. Add the pork belly and coat each side.

Add the remaining ingredients to the pot and bring to a slight boil. Cover, transfer to the oven, and bake for 30 minutes. Increase the heat of the oven to 375°F and remove the cover. Bake for another 4Stir the contents every 15 minutes.

Remove the pot from the oven and place on the stove over medium-low heat. Remove the pork and place on a plate. Carefully remove all the other ingredients and toss. Combine the cornstarch and water in a small bowl. Add to the sauce and mix until thickened. Toss the pork pieces in the sauce.

Preheat oven broiler. Slice the buns in half and place on a baking sheet. Combine the black garlic, butter, and shichimi togarashi. Spread the inside of each of the buns with the combined butter. Place under the broiler and toast until the buns have crisped up.

To assemble, add a portion of mayo to the bottom bun and then top with lettuce. Add a third of the pork belly. Top with a third of the sliced eggs and then the top of the bun.