Heat a cast iron skillet over medium-high heat for a few minutes until very hot.
Cut the lemon in half and then cut a ¼-inch-thick round slice from one half.
Place the lemon halves and the slice into the pan cut sides down and cook for about three to four minutes, until nicely charred.
Remove lemon from pan and add thyme sprig. Cook for about a minute, until fragrant, then set aside to cool.
Squeeze juice from lemon halves through a fine-mesh sieve into a small bowl.
Measure out 1 ½ ounces (45 ml) juice, reserving any extra for another use.
Stir honey into lemon juice until dissolved.
Fill a cocktail shaker with ice.
Pour in lemon juice mixture, gin, and vermouth and shake well.
Place a few ice cubes into a single old fashioned glass and strain drink into glass.
Garnish with charred lemon slice and thyme sprig. (Bruise the thyme with your fingers a bit so its flavors will infuse into the drink.)