A little dilution from a good stir helps tame this spirit-forward aperitivo or late-night sipper, which mellows and becomes more pleasurable as you sip
Dilution and keeping the proportion of absinthe to a bare minimum do seem to be key here. So much so that I thought maybe just an absinthe rinse would be enough, and then thought why stop there, and substituted rye for the cognac. The result is quite good, but obviously not the same cocktail - one could call this variation the “Martinezerac.”
Per the comment from Simon about dilution, I tried serving with a single large ice cube in a rocks glass and sipping it, there is definitely an optimum dilution and it's more than you think. I'd also suggest using a dropper for the absinthe and tasting, it can quickly overwhelm the drink.
A refined sweet martini. Excellent. Sampled this with Cocchi Dopo Teatro - I think it probably needs a rich vermouth - and Ableforth's Bathtub gin. This recipe is a keeper.