Melt half of the butter in a large pan over medium-high heat. Add the peppers and onion and cook 3-4 minutes or until softened.
Remove the vegetables from the pan and cover to keep warm.
Melt the other half of the butter and add the rib eye to the pan. Season with salt and pepper to taste.
Cook the steak for 3-4 minutes or until browned and just cooked through.
Place the peppers and onions back into the pan with the steak.
Lay out an egg roll wrapper and place 1/2 of a slice of cheese in the center.
Spoon approximately 2-3 tablespoons of steak filling onto each egg roll wrapper and fold according to package directions, using water to seal the edges of the wrappers as you go.
Pour 2-3 inches of oil into a deep pan. Heat the oil to 350 degrees.
Fry 3-4 egg rolls at a time, turning occasionally until browned all over, approximately 3-5 minutes.
Drain on paper towels, then serve with a dipping sauce of your choice.