Blend at high speed for 5 seconds or under, pour unstrained into something tall and add ice to top. Garnish.
Martin Doudoroff, in his Tiki+ app, speculates that the sarsaparilla may be a nod to the soda fountains of Don's youth. I think they may be inspired by the mauby (sometimes "mavi") tree bark-based sodas popular throughout the Caribbean, which share flavor notes in common with sarsaparillas and root beers.
Jeff Berry, Beachbum Berry's Sippin' Safari, p. 36.