Wash, peel and pit the peaches and then roughly chop them. Place in a large bowl, add the sugar and toss to combine. Cover with a clean cloth and let sit out overnight, stirring occasionally. Line a strainer with cheesecloth and set over a wide mouth jar or other container. Ladle the fruit into the strainer and let the liquid strain through. Press on the fruit to get as much juice as possible. (At this point, I stored the fruit in the freezer for smoothies.) Add the vinegar to the peach liquid. Cap and store in the fridge. This makes enough shrub to make several cocktails - it's also good mixed with carbonated water for a refreshing drink.
For the Cocktail:
Put all the ingredients in a cocktail shaker and shake vigorously until the egg white is foamy. Add some ice and shake again for 30 seconds. Strain into a cocktail glass filled with ice.
Notes
The calorie count on this recipe was tricky because the recipe makes a large amount of shrub. I used a combination of simple syrup and vinegar to come up with a close enough amount. Requires a day for shrub to infuse.