Combine the pisco, lime juice, simple syrup, and egg whites in a shaker without any ice.
Shake hard for 30-60 seconds, or until the egg whites are foamy.
Add ice to shaker and shake hard for another ten seconds, or until ingredients are sufficiently chilled.
Strain the chilled mixture from your shaker into chilled martini glasses, or any cocktail glass you have on hand.
Top with a few drops of Angostura bitters on top of each glass.