To make this refreshing, summery cocktail, start by making the Bubblegum-infused Aquavit at least 24 hours ahead of time. Quarter the bubblegum pieces and place them in a sealable glass jar. Add the 2 cups of aquavit, seal the jar and place in a cool dark place. Stir every 4 hours for the next 24 hours, except for overnight when you can allow the mixture to sit. After 24 hours, strain out the pieces of gum through a paper coffee filter or strainer.
Next, make the Spearmint Syrup, adding 1.5 cups of sugar and 1 cup of water to a small saucepan and heat on medium to a light rolling boil. Let the mixture cool and then add in 6 drops of spearmint oil, adding extra for a super minty syrup or less for a milder flavor.
Add moonshine, bubblegum-infused aquavit, lemon juice, lime juice, spearmint syrup and egg white to your shaker and shake vigorously without ice for 20 seconds. Add 3 ice cubes and shake vigorously again for at least 30 seconds. Strain into chilled coupe or cocktail glass.