Ramen Burger

Cook the Ramen: Bring a pot of water to a boil and add the ramen noodles. Cook until tender, stirring occasionally (approximately 3 minutes). Drain well and let cool slightly.

Prepare Ramen Buns: Beat 2 of the eggs in a bowl and season with salt and pepper. Stir the cooked ramen noodles into the egg mixture until evenly coated. Divide the noodle mixture into 6 equal portions, shaping them into burger-sized patties in ramekins or bowls. Cover with plastic wrap and press down firmly using another bowl or weight. Refrigerate until firm (about 20 minutes).

Season the Beef: In a bowl, combine the ground beef, soy sauce, and sesame oil. Mix well and divide the mixture into three equal portions. Shape each portion into a patty.

Fry the Ramen Buns: Heat about 1 tablespoon of vegetable oil in a large skillet over medium-high heat. Carefully invert each ramekin/bowl, gently tapping the bottom to release the ramen 'bun' while maintaining its shape.

Cook the Ramen Buns: Fry each ramen bun in the hot oil until golden brown (approximately 3 minutes per side). Flip and continue frying until crisp (3-5 minutes more). The ramen bun should be crispy on one side and slightly softer on the other. Transfer to a plate with the crispy side facing up.

Cook the Beef Patties: Heat another tablespoon of vegetable oil in the same skillet over medium heat. Cook the beef patties until lightly pink in the center (3-5 minutes per side). An instant-read thermometer inserted into the center should read 140 degrees F (60 degrees C). Place a slice of American cheese on each burger and cook until melted (about 1 minute).

Assemble the Burger: Mix the ketchup and chile-garlic sauce in a small bowl. Spread this mixture over the crispy side of each ramen bun. Divide the arugula evenly over 3 of the ramen buns. Place a cheeseburger on top of the arugula on each bun.

Fry the Eggs: Heat about 1 teaspoon of oil in a small skillet over medium-high heat. Fry the remaining egg, adding more oil if needed, until the yolk is almost firm (about 1 minute per side). Place the fried egg over the patty and top with the remaining ramen bun.