Fill a tall chilled glass with ice and stir until the glass just starts to form dew on the outside, about 15 seconds. Pour out the ice. Add the gin and vermouth, then add the ice back and stir vigorously with a bar spoon for 15 seconds. Strain into a chilled martini glass. Twist the lemon peel over the drink, and rub the edges of the glass. Garnish with the lemon peel.