In a large heatproof pitcher, combine tea bags, boiling water, and the 1/2 cup mint leaves. Let steep for 5 minutes. Remove and discard tea bags and mint. Cover tea; let stand for 1 hour. Stir in apricot nectar and vanilla. Cover and chill for 4 to 48 hours.
To serve, fill tall glasses with ice cubes. Fill with tea mixture. If desired, garnish with apricot wedges and/or mint sprigs.