Combine 2 1/2 cups milk and ginger in a medium saucepan; bring to a simmer over medium heat, stirring frequently. Remove from heat; let stand 5 minutes.
Combine 1/2 cup milk, sugar, cornstarch, salt, and egg yolks in a medium bowl, and stir with a whisk until well-blended. Gradually stir one-fourth of the hot milk mixture into egg mixture; add to remaining milk mixture, stirring constantly. Bring to a boil over medium heat; cook 1 minute or until thick and creamy, stirring constantly. Remove mixture from heat; stir in butter, rind, and vanilla. Pour into a bowl; cover surface of the pudding with plastic wrap. Chill.