Heat the milk until steaming, remove from heat, and steep the tea for 15 minutes. Strain and cool to room temperature.
Preheat oven to 325 degrees F. Grease a baking dish and set it inside a larger roasting pan.
Whisk the egg yolks with half the sugar until pale and thickened. Whisk in the melted butter, then the cooled chai milk and vanilla.
Sift in the flour, cinnamon, cardamom, ginger, cloves, and salt. Whisk until smooth. The batter will be thin.
Beat the egg whites until foamy, gradually add the remaining sugar, and beat to soft peaks.
Fold a third of the egg whites into the batter to lighten it, then gently fold in the rest, stopping while white streaks are still visible.
Pour into the prepared dish. Add hot water to the roasting pan until halfway up the sides of the baking dish. Bake for 45 to 50 minutes, until the top is set but slightly jiggly in the center.
Cool completely, then refrigerate at least 2 hours before slicing.
Dust with powdered sugar just before serving.