In a small bowl, whisk flour, granulated sugar, baking powder, and salt to combine.
In a medium bowl, whisk eggs, butter, and anise to combine. Add dry ingredients to butter mixture and stir until incorporated. Cover bowl with plastic wrap and chill at least 30 minutes or up to 1 hour.
Preheat oven to 350°. Line 2 baking sheets with parchment. Roll dough into 1-ounce balls (about 1 heaping tablespoon), lightly dusting with flour to prevent sticking. Arrange balls on prepared sheets and slightly flatten with the palm of your hand. If you’re using a cookie stamp, press into dough to create an indentation.
Bake cookies, rotating sheets top to bottom halfway through, until lightly golden on the bottom and edges are crispy, 20 to 22 minutes.
Let cool completely on sheets. Dust with powdered sugar.