An Etymological Dictionary of the German Language/Brühe
Brühe, f., from the equiv. MidHG. brüeje, ‘broth, sauce.’ The root of the word must not he sought in brauen, which is based upon bru-; brü-je would be in Goth. brôja, Teut. root brô, in MidE. brêie, MidDu. broeye. From the same stem MidHG. Brut has been formed, with a dental suffix. The wk. vb. is brühen, MidHG. brüejen, brüen, ‘to scald, singe, burn’; comp. Du. broeijen, ‘to warm, brood’; in earlier ModHG., too, brühen signifies ‘to brood,’ In spite of the meaning, the connection with Bruch is, on phonetic grounds, improbable.