Heat oven to 325ºF with rack set in middle position. Line an 8½ × 4½-inch loaf pan with parchment paper, leaving a 2-inch overhang on two sides.
Process 1 ¼ cups (160g) pistachios, 1 cup (200g) sugar, and ½ teaspoon salt in a food processor until finely ground into a powder, but not a paste, about 1 ½ minutes; scraping down sides and bottom halfway through.
Pulse 8 tablespoons butter into pistachio mixture (10 pulses), then process until the mixture is clumpy yet smooth and shiny, about 2 minutes, stopping to scrape down sides of bowl halfway through. (The mixture will go from very loose and batter-like to clumpy yet shiny—this is what you want.)
Stream in 3 eggs (150g) and ⅓ cup (85g) buttermilk and blend to combine, 1 minute. Add 1 teaspoon vanilla extract and ½ teaspoon almond extract; process to combine.
Add 1 cup + 2 tbsp (145g) whole-wheat flour, 1 ¼ teaspoons (6g) baking powder, 1 teaspoon ginger, and ¼ teaspoon cardamom; process just until combined.
Pour batter into prepared loaf pan. Sprinkle granulated sugar over top (1–2 tablespoons). Transfer to oven and bake until cake is tall, browned, and a toothpick inserted in the center comes out clean, 65–72 minutes.
Let cake cool in pan on rack for 15 minutes, then run a knife around cake and use parchment overhang to lift cake out of pan; transfer to cooling rack and cool completely.