Combine all ingredients in a dry cocktail shaker. Secure the lid and shake vigorously for about 20 seconds. (This is a "dry shake" without ice.)
Fill the shaker halfway with ice. Secure the lid and shake vigorously for another 20 seconds.
Strain the cocktail between two chilled coupe glasses and garnish with dehydrated lemon or orange wheels, or a fresh lemon twist.
Notes
Simple syrup is equal parts sugar and water. I combine 1/4 cup of sugar with 1/4 cup of very hot water in a small mason jar, tightly secure the lid, and shake for about 30 seconds until the sugar is mostly dissolved. It will last in the refrigerator for up to two weeks!*For an Aperol Sour with no egg, simply omit the egg white OR substitute it with two teaspoons aquafaba (liquid from a can of chickpeas).