To make the cookies: In a medium bowl, whisk the four, baking powder, and salt together and set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream the butter and sugar together on medium speed until creamy and light, about 2 minutes. Beat in the egg and egg yolks, one at a time, scraping down the sides after each addition, followed by the vanilla extract, anisette, and orange zest. Beat in the dry ingredients on low speed to form a stiff dough. Remove the dough from the bowl, flatten it into a disk, wrap it in plastic, and chill until it is firm enough to roll, about 1 hour.
Preheat the oven to 350°F. Lightly grease two baking sheets with nonstick cooking spray or butter or line them with parchment paper.
Divide the dough into 3 equal pieces; work with 1 piece at a time, keeping the remaining pieces refrigerated. On a floured surface, roll the dough to a thickness of 1/8 inch. Using a floured 2-inch star-shaped cookie cutter, cut the dough into stars. Place the cookies ½ inch apart on the baking sheets. Gather the scraps together and repeat rolling and cutting until you have used all the scraps; it may be necessary to refrigerate the scraps until they are firm enough to roll again.
To make the glaze: In a small bowl, whisk the egg yolk with the cream. Using a small pastry brush, lightly brush the surface of the cookies with a bit of glaze and decorate them with the sprinkles.
Bake the cookies until they are lightly golden brown, 12 to 14 minutes, rotating the baking sheets 180 degrees halfway through the baking time to ensure even browning. Allow the cookies to cool slightly on the baking sheets, then gently remove them with a spatula to a wire rack to cool completely.
The cookies can be stored in an airtight container, layered between sheets of parchment paper, for up to 4 days.