Whisk the all-purpose flour, semolina flour, baking powder, baking soda and salt in a large bowl. In a separate bowl, beat the butter and sugar with a mixer on medium speed until light and fluffy, about 2 minutes.
Whisk the olive oil, whole egg, egg yolk, limoncello, vanilla, lemon zest and lemon juice in a large liquid measuring cup or bowl. Add to the butter mixture and beat on medium speed until smooth. Reduce the mixer speed to low; add the flour mixture and beat until just combined. Cover the dough with plastic wrap and chill 30 minutes.
Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper. Roll the dough into 2-inch-long, 1/2-inch-thick logs; arrange about 2 inches apart on the prepared baking sheets. Bake in batches until golden around the edges, about 18 minutes, rotating the baking sheets halfway through. Let cool 2 minutes on the baking sheets, then transfer to racks to cool completely.
Meanwhile, put the white chocolate in a heatproof bowl and set over a saucepan of barely simmering water (do not let the bowl touch the water); stir until the chocolate melts. Drizzle the cookies with the melted white chocolate and sprinkle with the pistachios. Let set at room temperature, about 15 minutes.
Photograph by Anna Williams
Recipe courtesy Food Network Magazine