Anise Cookies

Whisk flour, baking powder, and salt in a medium bowl. Using an electric mixer on medium speed, beat eggs, granulated sugar, butter, oil, and 1½ tsp. anise extract in a large bowl until smooth, light, and foamy, about 2 minutes. Reduce mixer speed to low and add dry ingredients; beat just to combine.

Roll tablespoonfuls of dough into balls with your hands. Space at least 1" apart on 2 large parchment-lined baking sheets. Chill until very firm, about 1 hour.

Arrange racks in upper and lower thirds of oven; preheat to 350°. Bake cookies, rotating sheets halfway through if coloring unevenly, until golden brown around the edges and tops are firm, 10–12 minutes. Let cool.

When cookies are cool, whisk powdered sugar, remaining 1 tsp. anise extract, and 3 Tbsp. water in a large bowl until smooth (glaze should be the consistency of heavy cream; add water by the teaspoonful to loosen if needed). Gently toss cookies in glaze until lightly coated, letting excess drip back into bowl. Transfer to clean parchment-lined baking sheets (you can use a small offset spatula for this, but the glaze is pretty forgiving of any finger marks) and let sit until glaze hardens, about 2 hours.

Do Ahead: Cookies, without glaze, can be made 2 months ahead; store airtight and freeze.