Place 4 of the thyme sprigs in a dry frying pan over medium heat and toast until fragrant, about 4 to 5 minutes.Muddle the toasted thyme, tea leaves, and lemon juice in a cocktail shaker until the thyme is gently crushed, about 5 seconds.
Add the elderflower liqueur, egg white, and vodka, plus enough ice to fill about halfway. Close and shake until frosty, about 20 seconds.
Pour through a fine-mesh strainer into the chilled glass and garnish with the lemon twist and remaining thyme sprig.
