brothyoudaoicibaDictYouDict[broth 词源字典]
broth: [OE] Broth comes ultimately from the Indo-European base *bhreu- or *bhru- ‘heat, boil’, which also produced brew and fervent. Etymologically, therefore, it means ‘liquid in which something has been boiled’. The notion of ‘heating’ has now disappeared, but it seems to have survived into the modern English period, as is shown by such compounds as snow-broth ‘melted snow’, first recorded at the end of the 16th century.

The Germanic form *brotham was borrowed into Vulgar Latin as *brodo, which came via Old French broez into 13th-century English as broys or browes. This survives in Scottish English as brose ‘type of porridge’, as in Atholl brose.
=> brew, fervent, imbrue[broth etymology, broth origin, 英语词源]
broth (n.)youdaoicibaDictYouDict
Old English broþ, from Proto-Germanic *bruthan (cognates: Old High German *brod), from verb root *bhreue- "to heat, boil, bubble; liquid in which something has been boiled" (source also of Old English breowan "to brew;" see brew (v.)). Picked up from Germanic by the Romanic and Celtic languages.

The Irishism broth of a boy, which is in Byron, was "thought to originate from the Irish Broth, passion -- Brotha passionate, spirited ..." [Farmer], and if so is not immediately related.