Prepare Pan: Line a half sheet-sized baking pan with parchment paper. Lay two sheets of edible wafer paper on top without overlapping. Set aside.
Mix Egg Whites: Pour egg whites into a stand mixer bowl with the whisk attachment. Set aside.
Preheat Oven & Prepare Syrup: Preheat your oven to 350°F (175°C). In a large saucepan, combine honey, corn syrup, water, and sugar. Wash any sugar crystals from the sides of the pan using a wet pastry brush. Cook over medium heat until the mixture starts to simmer, around 4 minutes. Clip a digital thermometer to the side of the pan.
Cook Syrup to Hard-Crack Stage: Continue cooking the syrup, keeping an eye on the thermometer. Once it reaches 310°F (154°C), remove it from the heat and let it cool to 300°F (149°C).
Whisk Egg Whites: While the syrup is cooking, beat the egg whites on medium speed until frothy. Add salt and powdered sugar, then continue beating until soft peaks form. Lower the mixer speed and wait for the syrup to cool to 300°F.
Combine Syrup and Egg Whites: Once the syrup hits 300°F, turn the mixer to high and slowly pour the syrup into the egg whites. Continue to beat for about 5 minutes, or until the mixture thickens and sticks to the beaters.
Warm Pistachios: Place pistachios in the preheated oven to warm them up for a few minutes. Turn off the oven and leave them inside.
Fold in Pistachios: With a spatula or large wooden spoon, fold the warmed pistachios into the nougat mixture.
Knead the Nougat: Dust a clean surface generously with cornstarch. Turn out the nougat mixture onto the surface, dust the top with more cornstarch, and begin folding and stretching the mixture. Repeat this process for 6 more turns, applying more cornstarch as needed to prevent stickiness.
Shape Nougat: Once the nougat is well-stretched and smooth, place it onto the edible wafer paper in the prepared pan. Top with another sheet of wafer paper.
Cool & Flip: Let the nougat cool at room temperature for about 2 hours, flipping it halfway through so the bottom layer of wafer paper is on top.
Cut & Store: After the nougat has set, use an oiled knife or kitchen shears to cut it into pieces. Store the pieces in an airtight container between layers of parchment paper for up to 2 weeks.