Combine all but soda and garnishes in shaker. Shake, strain into tiki mug full of crushed ice; add soda. Garnish with mint leaves.
The original recipe (see source reference) did not include Armagnac. The Armagnac is an enhancement by Paul McGee while at Three Dots and a Dash, Chicago; it appeared in the ingredients list on the Three Dots menu (and the amount of 1/2 ounce was confirmed by other sources).
Navan vanilla liqueur is extremely expensive and hard to find. I have used Tuaca as a substitute; others recommend Licor 43.