Bring a small pot of water to a boil over high heat; prepare a bowl of ice water. Gently add the 2 whole eggs (in their shells) to the boiling water and cook for 8 minutes. Drain and transfer to the bowl of ice water immediately. When cool enough to handle, peel, slice and set aside.
Fill the same small pot with water and bring to a boil over high heat. Add the bacon and boil until some of the fat has rendered, about 4 minutes. Drain and set aside.
Preheat the oven to 350 degrees F.
Bring another small pot of water to a boil over high heat. Add the ramen noodles and cook for 30 seconds. Immediately drain the ramen and combine with the beaten egg in a medium bowl.
Brush the inside of large cast-iron skillet all over with the oil. Mound the ramen in the center of the skillet. Place a smaller skillet, around 6 inches in diameter, on top of the mound and press down firmly. Let sit for 5 minutes. Remove the smaller skillet and transfer the cast-iron skillet with the ramen onto a burner over medium heat. Cook, shaking the skillet occasionally to avoid sticking, until the ramen bottom is golden and crispy, about 5 minutes.
Flip the ramen with a spatula. Remove the skillet from the heat and top the ramen with the mayonnaise, tonkatsu sauce and hot sauce. Top the sauces with the cabbage, radish, bean sprouts and scallions.
Bake until the toppings are warmed through, about 5 minutes. Transfer the pizza out of the cast-iron skillet onto a cutting board. Top with the seaweed snacks, togarashi, soft-boiled eggs, pickled ginger, bacon and finger chile. Cut into wedges and serve immediately.
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