Heat two tablespoons of unsalted butter in a small saucepan over medium heat. Cook the butter until it starts to foam, whisking frequently as it cooks. (The color still start to change into a brown hue). Continue cooking and whisking until all of the butter is browned and has a nutty aroma. Remove the pan from the heat immediately and transfer the butter to a shallow, non-reactive dish that has a lid. Allow the browned butter to cool briefly, then stir the bourbon into the dish to combine the two together.
Seal the container and let it rest at room temperature for 1-2 hours. Pop it into the freezer for at least 3-4 hours, but up to overnight. The butter will separate from the bourbon, but will infuse the bourbon with its flavor. Strain the bourbon through a fine mesh sieve or cheesecloth into a container in which you’ll store it. Discard the butter.
To Make the Spiced Honey Syrup:
Combine the water and honey in a small sauce pan over medium-low heat. Add whole cloves, black peppercorns, and cinnamon. Stir to combine, then until the honey is dissolved into the water. Remove the pan from the heat and let it rest at room temperature for 30 minutes. Strain the honey syrup into a storage bottle, and discard the cloves and peppercorns.
To Make the Cocktails:
Combine brown butter bourbon, fresh grapefruit juice, spiced honey syrup, fresh lemon juice, bitters, and egg white into a large cocktail shaker. Dry shake (without ice) for about 20 seconds. Add a handful of ice to the shaker, then shake for another 20 seconds. Strain the cocktail through a fine mesh sieve into two chilled coupe glasses (or glassware of your choice), and garnish with dehydrated citrus or a grapefruit twist.
Notes
The Brown Butter Bourbon will keep in the refrigerator for up to a month.Egg White can be substituted with Aquafaba (which is the liquid in a can of chickpeas). I recommend using one teaspoon of aquafaba per cocktail if you choose to use it as a substitute.