This, er, annoyingly cliché'd but Grade I Listed terrace was designed in 1833 by Joseph Hansom, more famous for designing the archetypal Victorian horse-drawn cab.
I hadn't realised that Hansom was an architect at all, never mind that he'd been responsible for important parts of Beaumaris, including the gaol (1829), Bulkeley Arms Hotel (1832, the year Princess Victoria herself stayed there) and Henllys Hall (1852). He was also the architect of Birmingham Town Hall (1831) which, as mentioned alongside the first photo in this set, was constructed using Anglesey's Penmon limestone.