Combine all ingredients, except for the peated scotch whisky, into a cocktail shaker. Fill the shaker with ice and shake for 7-10 seconds to chill. Strain the cocktail into a rocks glass over ice, and float the peated scotch whisky on top. Garnish with candied ginger.
HONEY GINGER SYRUP:
In a medium saucepan, combine 3/4 cup of water and 1/4 cup of freshly chopped ginger. Add in 1.5 cup of honey, and bring the mixture to a light simmer over medium-high heat. Gently stir to combine the honey, water and ginger. Remove from heat to let the syrup cool. Strain the mixture through a fine mesh strainer, discarding solids. Store in a glass jar in the refrigerator up to 2 weeks.