Bring 2 ½ cups water to a boil in a saucepan over medium-high heat. Remove the saucepan from the heat. Gently stir in ½ cup Thai black tea leaves and let steep for 5 minutes.
Pour through a fine-mesh strainer or cheesecloth set over a heatproof bowl; discard the tea leaves. Stir ¼ cup granulated sugar and ¼ teaspoon kosher salt into the tea base until dissolved. Let cool to room temperature, about 10 minutes.
For each cocktail, pour a quarter of the Thai tea base (scant ½ cup) into a tall glass. Stir in 1 tablespoon sweetened condensed milk until dissolved. Fill the glass halfway with ice and stir to combine. Top with ¼ cup vodka and then ½ cup chilled sparkling water for a layered look. Garnish with 1 fresh mint sprig if desired. Stir together before drinking.
