Stir 1 1/2 ounces gin, 1 ounce Carpano Antica Formula vermouth, and 3/4 ounce Campari in an ice-filled mixing glass until very cold, about 30 seconds. Strain cocktail through a Hawthorne strainer or a slotted spoon into an ice-filled rocks glass. Using a small serrated knife, remove a 1″ strip of peel from an orange (some white pith is okay); it should be stiff enough to provide some resistance when bent. Twist over drink to express oils; discard. Garnish with 3 very thin orange slices.