Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.

Combine flour, sugar, eggs, egg yolk, baking powder, and vanilla extract in a food processor. Blend until the mixture forms a ball, scraping the sides of the bowl once or twice. Turn mixture onto a lightly floured surface and knead in hazelnuts, almonds, and anise seeds.

Beat egg yolk and water together in a bowl.

Divide dough into 3 pieces and roll into logs about 1 1/2 inches wide. Place onto the prepared baking sheet at least 2 inches apart. Brush with egg yolk-water mixture.

Bake in the preheated oven for 30 minutes.

Remove from oven and reduce heat to 300 degrees F (150 degrees C). Cut logs diagonally into 1-inch slices and lay cut-sides down on the baking sheet. Return cantuccini to the oven until dry and firm, 30 to 40 minutes more.