In a shaker combine Aperol, gin, lemon juice, simple syrup, egg white. Dry shake for a few seconds (without ice).
Open the shaker carefully, add in some ice. Shake until cooled.
Strain into chilled coupe glass.
Notes
The dry shake makes extra-thick egg foam, but you can skip it if you like. You'll still get foam if you shake with ice directly, it'll just be a bit diluted/not as dense.