Famous New Orleans Drinks and How to Mix 'Em by Stanley Clisby Arthur (1938, p.31)

1.5 jiggerrum — Rumbase
1 wholesugar — Loaf sugarbase
1 wholeOrange peel — Orange peelgarnish
mint — Mint sprigsother
shaved ice — Shaved iceother
  1. Moisten the sugar with a little water in a tall glass or metal goblet and crush it while muddling several mint leaves.
  2. Fill with shaved or finely crushed ice, pour in the rum, jiggle to frappe, top with a bouquet of mint, and garnish with orange peel if desired.

Garnish: Mint bouquet and optional orange peel

Ice: Shaved ice

Arthur explicitly treats this as the earlier rum-based julep brought from San Domingo to Louisiana in 1793.