Combine the sugar and crystallized ginger in a food processor and process until very fine.
Bring the milk to a bare simmer in a medium saucepan over medium-low heat.
Whisk the egg yolks, cornstarch and ground ginger together in a large bowl. Slowly whisk in the hot milk mixture, taking care not to scramble the eggs. Return the mixture to the suacepan and cook over medium heat until very thick, 3 to 5 minutes. Transfer to a bowl, straining if necessary to remove any chunks. Stir in the crystallized ginger mixture, then cover with a sheet of plastic wrap pressed directly against the surface of the pastry cream to keep a skin from forming. Refrigerate until chilled.
Beat the pastry cream in a stand mixer fitted with the paddle attachment until smooth before using.