1/2 cup Kalbi-style Korean steak marinade, or as needed
2 tablespoons oil, divided
2 cups chopped onions
1 cup diced jalapeno peppers
1/2 cup chopped kimchi
1 cup shredded American cheese
1/4 cup mayonnaise
4 sandwich rolls, split and toasted
Mix beef and marinade together in a bowl; set aside to marinate. Heat 1 tablespoon oil in a skillet over medium-high heat; saute onions until lightly golden but still firm, 5 to 10 minutes. Heat 1 tablespoon oil in a separate skillet over medium-high heat; saute jalapeno peppers until very lightly golden, about 5 minutes. Mix jalapeno peppers into onions. Add kimchi and cook until heated through, 2 to 3 minutes. Remove skillet from heat. Heat a separate skillet over medium-high heat and cook steak, stirring constantly, until browned and cooked through, about 5 minutes. Return 3/4 cup kimchi mixture to skillet over medium heat; add 1/4 cup American cheese. Cover skillet and heat until cheese is melted, 2 to 3 minutes. Spread 1 tablespoon mayonnaise onto the bottom half of 1 roll and top with 1/4 of the beef. Layer kimchi-cheese mixture on top of beef and top with roll. Repeat with remaining ingredients to create 3 more sandwiches.