v1.0
Publishing history:
v1.0: 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).
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).
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’.
Derivatives: with the nominally diminutive suffix -an: SG brodan ‘small goad etc.’ (AFB˄), (Easter Ross) /brɑdɑn/ ‘poker’ (Watson 2022, 128, s.v. brodan).