Classically the Stinger is shaken and served straight-up in a chilled coupe. However, I think it makes for a more refreshing peppermint and brandy digestif...
I originally made this in 2020 using a 2:1 ratio and thought the creme de menthe was just too much. Just made the above recipe, essentially serving up and thought it was decent, and probably better over more ice. Tried it again at a 3:1 then 4:1 ratio, and the former turned out to be perfect for an up serving. 4:1 the mint is there, but the harmony is dissonant.
I think this modernized version is much better than the equal parts original - I would even increase the cognac slightly to 2.25 oz / 67.5 ml - but it's still an intensely minty cocktail that bares for me an unfortunate association with toothpaste. My favorite version dials the Creme de Menthe way down - 2 oz / 60 ml cognac with 0.25 oz / 7.5 ml creme de menthe - for more of a minty cognac Old Fashioned feel.