Place pistachios in the bowl of a food processor. Pulse until the nuts are in small bits. Add the sugar and water, and blend until relatively smooth.
To make the Pudding:
1) Spoon Pistachio Paste into a medium saucepan. Add the milk and whisk over medium heat. Heat milk and pistachio until steamy and hot.
2) While milk is heating, whisk together granulated sugar, egg yolks, cornstarch and pinch of salt. Mixture will be thick. Keep whisking until it’s smooth. Pour about 1/2 cup of the steaming pistachio milk into the sugar and egg mixture. Whisk together. Add another half cup of hot milk and whisk to incorporate. Return the milky egg mixture into the saucepan over medium heat.
3) Heat pudding mixture over medium heat until thick and bubbly. Whisk almost constantly. You might also want to use a heat-proof spatula to stir the mixture, ensuring that the sides and corners of the pan aren’t burning. Boil for about 1 minute, or until thickened. Remove from heat and stir in butter and vanilla extract, until butter is melted. Pass cooked pudding through a fine mesh strainer set over a medium bowl. This will ensure that any cooked egg bits don’t make it into the finished pudding. Press the pudding through the strainer. Add a few of the pistachio nut bits that the strainer catches back to the pudding if you’d like.
4) Spoon into small ramekins, place plastic wrap over the individual puddings (so the plastic touches the top of the pudding), and refrigerate for at least 4 hours, or overnight.
5) Top with lightly sweetened whipped cream and chipped pistachios. Pudding will last, covered in the refrigerator, for up to 4 days.