In a pot, cook Maruchan noodles in boiling water for 3 minutes. Add seasoning packets. Strain noodles.
Beat 2 eggs. Add a pinch of salt and pepper.
Add noodles to egg and mix until evenly coated. Divide into 6 small bowls and cover. Ensure noodles are flattened and refrigerate for 20 minutes.
Heat vegetable oil over medium heat and cook ramen for 3 minutes on each side or until crisp.
Mix beef, soy sauce, and sesame oil in bowl. Shape into 3 patties.
Cook beef patties for 3 to 5 minutes on each side until center is lightly pink (or as desired). Add 1 slice of American cheese on top and cook for 1 minute more.
Fry 3 eggs in pan until yoke is firm and place on top of each patty.
Mix ketchup and Sriracha together.
Assemble burger with ramen buns, Sriracha and ketchup mixture, arugula, beef patty, and egg.
DISCLAIMER: Consuming raw or undercooked eggs, meats, poultry, seafood or shellfish may increase your risk of foodborne illness, especially if you have certain medical conditions.