Ramen Bun Burger

Begin by placing a pot of water on the stovetop and bringing it to a rolling boil. Next, add the ramen noodles to the pot and continue boiling, occasionally stirring the mixture, until the noodles have reached your desired level of tenderness - typically around 3 minutes. Remove the pot from the heat and let the noodles cool down slightly.

In a separate bowl, whisk together 2 eggs until they're fully incorporated. Add a pinch of salt and pepper to the eggs, then mix them together until they're evenly coated. Combine the cooked noodles with the egg mixture and divide the noodle-egg mixture into 6 individual serving portions.

Place a sheet of plastic wrap directly over each noodle portion and stack another bowl on top to help flatten the noodles. Refrigerate the noodles for about 20 minutes, allowing them to firm up and hold their shape.

Meanwhile, combine the beef, soy sauce, and sesame oil in a bowl. Divide the beef mixture into three equal parts and shape each portion into a patty.

Heat about 1 tablespoon of vegetable oil in a large skillet over medium-high heat. To assemble the ramen buns, invert each noodle portion and gently tap the bottom of the bowl to loosen it. Be careful not to disturb the noodles, as you want them to remain intact.

Fry each ramen bun in the hot oil until it's golden brown and crispy, about 3 minutes. Flip each bun over and continue frying for another 3 to 5 minutes, or until it's crispy on one side and slightly softer on the other. Transfer the buns to a large plate with the crispy side facing up.

Heat another 1 tablespoon of vegetable oil in the same skillet over medium heat. Cook the beef patties until they're lightly pink in the center, about 3 to 5 minutes per side. Use an instant-read thermometer to check the internal temperature of the patties, aiming for 140 degrees F (60 degrees C). Top each patty with a slice of American cheese and continue cooking until the cheese is melted, about 1 minute more.

Mix together ketchup and chile-garlic sauce in a small bowl, then spread the mixture over the crispy side of each ramen bun. Divide some arugula among 3 of the buns, then place a beef patty on top.

Heat about 1 teaspoon of oil in a small skillet over medium-high heat, then fry the remaining eggs one at a time until they're almost firm. Place each egg over a beef patty and top with the remaining bun.