Make the peanut-infused bourbon: Place the unsalted peanuts and the bottle of bourbon in a food-grade plastic container. Let steep for 24 hours. Strain the peanuts from the container, then pour the bourbon back into the bottle. Freeze the bottle of bourbon for 24 hours. While the liquid is still frozen, scoop off the fat that has risen to the top.
Make the honey syrup: In a small bowl, mix together the honey and water until the honey is well dissolved.
In a mixing glass filled with ice, add the bitters, ¼ ounce of the prepared honey syrup and 2 ounces of the prepared peanut-infused bourbon. Stir well, about 20 seconds. Strain into an Old Fashioned glass with one large ice cube. Garnish with an orange peel. Serve.