In a small saucepan, combine honey, water, and sliced ginger.
Bring the mixture to a boil over medium heat, then reduce the heat and simmer for 5 minutes.
Remove from heat and let it cool. Strain the syrup into a container, discarding the ginger slices.
In a cocktail shaker filled with ice, combine blended Scotch whisky, lemon juice, and 3/4 ounce of the honey-ginger syrup.
Shake well until chilled and strain into a rocks glass filled with fresh ice.
Gently pour the Islay single malt Scotch over the back of a spoon to float it on top.
Enjoy your Penicillin cocktail garnished with an optional lemon twist.