How to Make It
In a medium bowl, combine the egg yolks, sugar, cornstarch, cinnamon, nutmeg, cloves and salt. Using a handheld electric mixer, beat at medium speed until the egg yolk mixture is thickened and light yellow, about 4 minutes.
In a medium saucepan, heat the milk and half-and-half until small bubbles appear around the rim. Gradually beat 1 cup of the hot milk mixture into the egg yolk mixture, then add the egg yolk mixture to the saucepan. Cook over moderate heat, stirring constantly with a heatproof rubber spatula, until the pudding is gently boiling and as thick as mayonnaise, 6 to 7 minutes. Remove from the heat.
In a small skillet, cook the pumpkin puree over high heat, stirring constantly, until slightly dry, about 3 minutes. Add the puree to the pudding along with the butter and vanilla and stir until the butter melts. Transfer the pudding to a large bowl and press a sheet of plastic wrap directly onto the surface. Refrigerate until very cold, about 4 hours.
In a large bowl, using an electric mixer, beat the heavy cream with the confectioners' sugar and minced crystallized ginger at high speed until firm peaks form.
Spoon the pudding into wine glasses or dessert bowls and dollop the ginger whipped cream on top. Sprinkle with the crumbled gingersnaps and serve.