Essex Quay must have been the most amazing place in the first half of the 19th Century. If you check through the street numbers in 'Wilson's Dublin Directory' at:viewtopic.php?t=16498
you will notice that the entire street was possibly the hub of the silver trade in Dublin, the missing numbers that I didn't include were the premises of such trades as Ivory Turners and the like.
William Brodrick is listed in the above Directory as a Watch & Clockmaker of 3, Essex Quay. He is noted as working out of 4, Essex Quay in 1818, 3, Essex Quay in 1827 and 12, Essex Quay in 1837, where he remained until 1866. He registered with the Dublin Assay Office in 1825.
As for the maker, my first thought was Samuel Green of Cork who was known to have his work assayed at Dublin, but I think he was dead by 1842. Samuel Garre is a possibility, he registered in 1828.