Blanch and peel the pistachios (blanched and peeled): Bring a small pot of water to a boil, add the pistachios, boil for 1 minute, drain, shock in ice water, then slip off the skins and pat dry.
Portion the dairy and sugar: From the measured whole milk (2 cups) and granulated sugar (0.75 cup), set aside 1 cup milk and 0.25 cup sugar for blending; reserve the remaining 1 cup milk and 0.5 cup sugar for the custard.
Make the pistachio paste: In a blender, combine the peeled pistachios with the set-aside 1 cup milk and 0.25 cup sugar; blend until very smooth, 1–2 minutes, scraping down as needed.
Heat the custard base: In a medium saucepan, combine the reserved 1 cup milk, the heavy cream, the reserved 0.5 cup sugar, and the fine sea salt. Cook over medium heat, stirring, until steaming and small bubbles form at the edges, 3–5 minutes.
Infuse the flavor: Stir in the pistachio paste, cover, and let steep off the heat for 20–30 minutes to deepen the pistachio flavor.
Prepare the eggs: In a medium bowl, whisk the egg yolks until smooth and slightly lightened, about 30 seconds.
Temper and cook: Rewarm the pistachio mixture until steaming. Slowly whisk about 1 cup of the hot mixture into the yolks, then return the yolk mixture to the saucepan. Cook over medium-low, stirring constantly with a heatproof spatula, until the custard thickens enough to coat the back of a spoon and reaches 170–175°F, 5–8 minutes; do not boil.
Finish and chill: Off heat, stir in the vanilla extract and almond extract. Strain through a fine-mesh sieve into a clean bowl. Set the bowl in an ice bath and stir until cool, 10–15 minutes. Cover and refrigerate until very cold, at least 4 hours or up to 24 hours.
Churn: Churn the cold base in an ice cream maker until it reaches soft-serve consistency, 15–25 minutes. In the last minute of churning, add the finely chopped pistachios to fold them in evenly.
Cure and serve: Transfer to a freezer-safe container, press parchment or plastic wrap directly on the surface, and freeze until firm, 4–6 hours. Let stand at room temperature for 5 minutes before scooping.