In a small food processor, add the pandan leaves and water and puree. Scrape down the sides as needed and resist the urge to add more water. It won’t look like it’s blending well, but you just want to get the pandan really pulverized.
Place a fine-mesh sieve over a liquid measuring cup and strain the mixture, pressing with a rubber spatula to extract the green liquid. You should have ¼ cup (60 g) pandan juice (if you’re short for whatever reason, just add a little water).
In a medium bowl, whisk together the pandan juice and cornstarch. Whisk in the egg yolks and set beside the stovetop.
In a large saucepan, whisk together the coconut milk, sugar, and salt. Heat over medium heat, whisking occasionally, until warm and steaming, about 5 minutes. Turn off the heat.
Gradually whisk the warm coconut mixture into the pandan mixture. Pour it back into the saucepan and cook over medium heat, whisking constantly, until thick like pudding, about 2 minutes. Remove from the heat and whisk in the shredded coconut, lime juice, butter, and coconut extract.
Scrape the filling into the cooled crust and spread into an even layer. Cover with plastic wrap so it touches the surface of the pudding (this will prevent a skin from forming). Refrigerate until chilled and set, at least 4 hours, but overnight is best.