Step 1

Place a rack in middle of oven; preheat to 325°. Grease a 9x5" loaf pan with vegetable oil, then line with parchment paper, leaving overhang on long sides. Oil parchment paper (for insurance and an easy release).

Step 2

Pulse pistachios in a food processor until finely ground (it’s okay if some of the pieces are a bit larger). Set aside a heaping tablespoonful.

Step 3

Whisk lemon zest, flour, granulated sugar, baking powder, salt, and remaining pistachios in a large bowl. Whisk olive oil, 2 Tbsp. lemon juice, remaining ⅓ cup vegetable oil, and ½ cup water in a small bowl to combine. Pour oil mixture into dry ingredients and fold with a rubber spatula to combine. Be very careful not to overmix: This batter contains a high ratio of liquid, which means it can get gummy if overworked. Transfer to prepared pan and use a spatula to distribute batter; batter should come halfway up the sides.

Step 4

Bake cake until golden brown all over, it springs back when gently pressed, and a tester inserted into the center comes out clean, 50–60 minutes. It's okay if your cake has dipped a little in the center. Transfer pan to a wire rack and let cake cool completely in pan, at least 2 hours. Using parchment overhang, lift cake out of pan and place on rack. Peel away parchment.

Step 5

Whisk powdered sugar and 3 Tbsp. lemon juice in a medium bowl, drizzling in remaining 2 Tbsp. lemon juice as needed until you have a thick but pourable glaze. Pour glaze over cake, letting it drip down the sides (if your cake has dipped, you can always glaze the flat underside instead of the top). Immediately top cake with reserved pistachios, then let sit until glaze is set, at least 30 minutes.

Step 6

Do Ahead: Cake can be made 3 days ahead. Store airtight at room temperature.