Add the white rum, apricot liqueur, triple sec, and lemon juice to a shaker without ice.
Add the egg white and dry shake vigorously for 15 seconds to emulsify the egg white and build foam.
Add a large scoop of ice to the shaker and shake hard for another 15 seconds until well chilled.
Fill an old-fashioned glass with fresh ice cubes.
Double-strain the cocktail through a fine-mesh strainer into the glass.
Garnish with an orange slice on the rim and serve immediately.
The reverse dry-shake technique - shaking with egg white before adding ice - maximises foam volume and creates a denser, more stable head than shaking with ice from the start.
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