Melt butter in a hot pot. Add onion; stir to coat. Add 1/4 cup beef broth; cook until broth is mostly absorbed, about 2 minutes. Stir in 3/4 cup broth and 1 cup water; bring to a boil. Add uncooked ramen without seasoning. Cook, uncovered, stirring, 2 to 3 minutes. Season with salt and pepper. Pour noodles and soup into a bowl, sprinkle with Gruyère and cover until cheese melts, about 1 minute.
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