Add navy rum, fresh lime juice, rich sugar syrup, chilled water, and aromatic bitters into a cocktail shaker.
Add ice and shake well for 10–12 seconds.
Strain into an ice-filled Double Old-Fashioned glass.
Garnish with a lime wedge and serve immediately.
Grog was officially ordered by British Admiral Edward Vernon in 1740 to dilute sailors' neat rum rations - the lime was a later addition that inadvertently prevented scurvy, making this one of the few cocktails that saved lives. The chilled water is non-negotiable: it's what separates grog from a rum sour and keeps it true to its naval origins.
My Bar Shelf reads your shelf and shows you every cocktail you can make from what you already own, including Grog.