Soak a used whiskey barrel with warm water for at least 48 hours to swell staves and prevent leaking. Combine the gin, Campari and vermouth in a large container to make a big batch of Negronis. Using a funnel, pour the mixture into a 2 ½ to 3 gallon Tuthilltown Spirits barrel and seal it.
After aging for at least 6 weeks, decant the barrel through a fine-mesh sieve into a large container to remove the sediment. Refill the barrel with water to prevent it from drying out. Decant the strained barrel-aged Negroni into bottles for service. Measure out the Negroni mixture with a jigger and pour into a chilled mixing glass. Add ice to the mixing glass. Stir with a barspoon until chilled. Strain the mixture into a chilled coupe. Mist with orange peel and serve.