Add the bourbon, coffee liqueur, and bitters to a mixing glass filled with ice.
Stir for 20 to 30 seconds until well chilled.
Strain into a chilled coupe, or over a large ice cube in a rocks glass.
To flame the peel, cut a wide strip of orange peel. Hold it skin side facing the drink, a few inches above the surface. Light a match or lighter next to the peel and give it a firm pinch. The oils spray through the flame, add a gentle caramelized orange aroma, and land on the drink. Rub the peel around the rim and drop it in.