In a shaker, combine gin, elderflower liqueur, lemon juice, and simple syrup.
Add the egg white to the shaker.
Dry shake (shake without ice) vigorously to emulsify the egg white.
Add ice and shake again until well-chilled.
Strain into a chilled coupe glass.
Wait for the froth to settle on top.
Gently place a few edible flowers on top of the froth for garnish.