Step 1

Place racks in upper and lower thirds of oven; preheat to 350°. Cook butter and bay leaves in a small nonstick skillet over medium-low heat, swirling occasionally, until milk solids are a deep amber color and butter smells very nutty, 6–8 minutes. (Be careful, it may sputter!) Fish out and discard bay leaves. Pour butter into a medium bowl, scraping in any browned bits. Set bowl with butter over a large bowl filled with ice water; let cool, stirring often, until slightly cooler than room temperature (not until hard), 15–20 minutes. (Or chill in fridge about 1 hour.)

Step 2

Meanwhile, toast ⅓ cup pistachios on a large rimmed baking sheet, tossing halfway through, until golden brown, 10–13 minutes. Let cool, then finely chop.

Step 3

Scrape butter into a large bowl. Using an electric mixer on medium-high speed, beat until light beige and fluffy, about 3 minutes. Reduce mixer speed to medium-low; beat in egg yolks and ½ tsp. vanilla, followed by ¾ cup (83 g) powdered sugar, scraping down sides of bowl as needed. Beat in chopped toasted pistachios and ¾ tsp. Diamond Crystal or ½ tsp. Morton kosher salt, then add flour in 2 additions. Beat until dough comes together. (It may look crumbly, but it should hold together when squeezed in your palm.) Transfer dough to a large piece of parchment paper and pat into a loose square. Cover with a second piece of parchment and roll out to a 9" square about ¼" thick. Chill dough 20 minutes.

Step 4

Uncover dough; cut into 1½"-wide strips. Cut strips at a 45° angle about 1½" apart, creating oblique diamonds. Arrange cookies on 2 parchment-lined baking sheets, spacing 1" apart. Bake, rotating baking sheets top to bottom and front to back halfway through, until edges are golden, 14–18 minutes. Let cool.

Step 5

Finely chop remaining 2 Tbsp. pistachios. Whisk a pinch of salt, remaining 2 cups (220 g) powdered sugar, remaining 1 tsp. vanilla, and 6–8 tsp. water in a small shallow bowl until thick and glossy (not runny, although it should drip off the whisk). Add more water or powdered sugar if needed.

Step 6

Working one at a time, dip tops of cookies in glaze, letting excess drip back into bowl; smooth with a spoon if needed. Sprinkle with pistachios and let sit 10 minutes to set.Do ahead: Cookies can be made 3 days ahead. Store air tight at room temperature.