Heat the oven to 350°F. Grease and line a 9-by-5-inch loaf pan with parchment.
Whisk the pistachios, flours, sugar, baking powder, and salt in a bowl.
In another bowl, whisk the eggs, melted butter, milk, lemon zest, and 1 tablespoon lemon juice.
Fold the wet mixture into the dry ingredients just until no dry streaks remain.
Scrape the batter into the pan and bake for 50 to 55 minutes, until the center springs back and a tester comes out with a few moist crumbs.
Cool in the pan for 15 minutes, then transfer to a rack and cool completely.
Whisk the powdered sugar with 1 to 2 teaspoons lemon juice and drizzle over the cooled loaf.