Prepare the Earl Grey tea-infused gin ahead of time: 

1. Add the tea leaves into the gin, cap and shake.
2. Let sit at room temperature for at least 2 hours and up to 8 hours.
3. Strain the infused gin through a coffee filter into a separate container.
4. Rinse the bottle to remove loose tea, and pour gin back into the clean bottle. Can be stored indefinitely if refrigerated.

Make and serve the cocktail: 

1. Use sugar to half-rim a coupe glass and set aside.
2. Add the tea-infused gin, lemon juice, simple syrup and egg white into a shaker without ice and dry-shake vigorously for at least 10 seconds.
3. Add ice and shake again until well-chilled.
4. Strain into the prepared coupe.
5. Garnish with a lemon twist.