Hot Penicillin

Bring honey, sliced ginger, and 5 cups water to a simmer in a medium saucepan over medium heat. Reduce heat and cook at a bare simmer, stirring occasionally, until honey is dissolved, 20–25 minutes. Strain through a fine-mesh sieve into a large measuring glass or a medium bowl (you should have about 4½ cups); discard solids. Pour honey syrup back into saucepan. Add blended Scotch, lemon juice, and single malt Scotch, if using. Heat over medium-low until hot but not boiling.

Divide cocktail among mugs. Run a toothpick or skewer through each piece of candied ginger and set over the mug’s rim to garnish.