v1.0
Published 01/10/24
brod m. [b̥ɾɔd̪̥], 
E.g. (Gairloch) [b̥rɔt] (Wentworth 2003, s.v. good: really good), but (North-West Sutherland) brad (Grannd 2013, s.v. ‘excellent’), (East Sutherland) /prad/ ‘good’ (Dorian 1978, 163, s.v. brad), (Easter Ross) /brɑd/ ‘choicest, the best’ (Watson 2022, 128, s.v. brod).
gen. bruid [b̥ɾɯ̟d̥ʲ], [b̥ɾɯd̥ʲ], ‘goad; prickle, sting; box for collecting alms in church; the best/choice/excellent part of something; lid’ (AFB˄) is from EG brot m. ‘goad, spike’.
While O’Rahilly (1942c, 169) takes EG brot (as well as Eng. brad) to be from ON broddr (leg. brodd acc.) m. ‘spike; barbed arrow or spear; pikestaff; front or leading part of something; shoal’ (cf. NO), 
Cf. Ó Muirithe (2010, 21).
Craigie (1894, 164) simply notes the similarity between SG brod, ON broddr and Scots brod (SND˄, s.v. 2brod ‘something with a point on, as a goad, a spur’) and McDonald (2009, 346) considers a derivation from Norse uncertain. Green (1972, 70), however, argues for a (cognate) Celtic origin, pointing out that OG brot in the sense ‘goad’ is attested in pre-Norse saga material, in the 8th-century law text Críth Gaḃlach and in the 9th-century St Gall glosses on Priscian, and a Celtic provenance is supported by Vendryes (1996) and apparently by Cameron (in MacBain 1894a, 621), MacBain (1911) and MacLennan (1925).
See also Pokorny 1959 II, 110.
This accounts for SG brod in the senses ‘goad; prickle, sting’ and EG brot. The senses ‘box for collecting alms in church’ and ‘lid’, however, presumably derive from Scots brod (SND˄, s.v. 1brod ‘board etc.’, senses 6 and 8).
The sense ‘best/choice/excellent part of something’, e.g. brod an t-sìl ‘the best part of the corn’, brod an taighe ‘a splendid house’ (Dwelly 1911) and brod ‘first born of a litter’ (Faclan bhon t-Sluagh˄: Inverness), is seen by MacBain (ibid.) as a semantic extension of ‘goad etc.’, via a sense ‘excess’, although a development via a sense ‘separating or winnowing’ also seems plausible, cf. the verbal noun brodadh m. ‘stimulating, searching, separating (HSS 1828); winnowing (Armstrong 1825)’ and the verb brod ‘to pick, separate the best parts (HSS)’.
Note that DOST˄ (s.v. 3brod vb) compares MScots brod ‘to clean (oats) from small or imperfect grains’ with the Scottish Gaelic noun brod and the verb brod in the sense ‘to separate peas from beans by means of a riddle’.
Any similarity with the extended sense of ON broddr ‘front or leading part’, e.g. í broddi lífs síns ‘in the prime of his life’, is likely to be fortuitous.
Derivatives: with the nominally diminutive suffix -an: SG brodan ‘small goad etc.’ (AFB˄), (Easter Ross) /brɑdɑn/ ‘poker’ (Watson 2022, 128, s.v. brodan).