An Etymological Dictionary of the German Language/Annotated/Brühe
Brühe, feminine, from the equivalent Middle High German brüeje, ‘broth, sauce.’ The root of the word must not he sought in brauen, which is based upon bru-; brü-je would be in Gothic brôja, Teutonic root brô, in Middle English brêie, Middle Dutch broeye. From the same stem Middle High German Brut has been formed, with a dental suffix. The weak verb is brühen, Middle High German brüejen, brüen, ‘to scald, singe, burn’; compare Dutch broeijen, ‘to warm, brood’; in earlier Modern High German, too, brühen signifies ‘to brood,’ In spite of the meaning, the connection with Bruch is, on phonetic grounds, improbable.