Place noodles in a saucepan filled with boiling water, reserving the seasoning packets. Cook until tender and drain. In a medium bowl, whisk together the eggs and seasoning packets from the noodles. Mix in noodles.
Melt butter in a large frypan over medium heat. Add the noodle mixture and cook over medium-low heat until firm, 5 to 7 minutes. Cut into quarters and turn over to brown the other side for 1 to 2 minutes. Sprinkle cheese over the top, and serve.