Cut 1 (2-inch) piece ginger (at least 1-inch wide) lengthwise into 3 slices (no need to peel), and place in a small saucepan. Add ½ cup honey, ½ cup water, and 1 pinch kosher salt. Bring to a boil over medium-high heat.
Transfer to a heatproof container and let cool until warm. Cover and refrigerate until cold, preferably overnight. Remove and discard the ginger before using.
Use a vegetable peeler to peel 1 long strip of peel from 1 medium lemon. Juice the lemon until you have ¾ ounce, then add to a cocktail shaker. Add 2 ounces blended Scotch whisky and ¾ ounce honey ginger syrup. Add enough ice to fill the shaker about half full. Seal the shaker and shake vigorously until the outside of the shaker is frosty, 30 seconds. (Alternatively, stir all the ingredients together in a mixing glass until very chilled, about 30 seconds.)
Fill a rocks or old-fashioned glass with ice. Pour the cocktail through a strainer into the glass. Top with ¼ ounce Islay single malt Scotch. Twist the lemon peel directly over the cocktail’s surface, then garnish with the peel.