1. Bring 4 cups water to a boil in a 3-qt. heavy saucepan; add tea bags. Remove from heat; cover and steep 10 minutes.
2. Discard tea bags. Add 1 cup sugar, stirring until dissolved. Bring tea mixture to a boil over medium-high heat, and cook, stirring occasionally, 20 to 22 minutes or until mixture is reduced to 1 cup. Remove mixture from heat, and let cool to room temperature (about 30 minutes).
3. Stir together mascarpone cheese, vanilla bean paste, and remaining 1/2 cup sugar.
4. Beat whipping cream at medium speed with an electric mixer until soft peaks form; fold into cheese mixture.
5. Separate ladyfingers in half. Arrange 24 ladyfinger halves, flat sides up, in the bottom of an 11- x 7-inch baking dish. Drizzle with half of tea mixture. Top with half of cheese mixture. Repeat layers once. Cover and chill 12 hours. Sift cocoa over top just before serving.