Preheat the Oven - Set the oven rack to the upper-middle and lower-middle positions. Preheat to 375ºF (191ºC). Line two large baking sheets with parchment paper and set aside.
Mix the Dry Ingredients - In a stand mixer fitted with the paddle attachment, mix the flour, sugar, baking powder, and salt until combined, about 30 seconds.
Mix in the Fats - Scatter the butter and shortening on the flour mixer. Mix on low speed (setting 2) until they break into very small pieces and look sandy, about 3 minutes.
Add the Wet Ingredients - Add the eggs, 1 teaspoon of anise extract, vanilla, and lemon zest. Mix on low speed (setting 2) until a dough forms, about 30 to 40 seconds.
Portion the Dough - Portion the cookie dough into 1 tablespoon-sized balls. Place them 2 inches apart, about 14 per baking tray.
Bake - Bake both trays at the same time for 7 minutes. Switch and rotate the pan positions. Bake until the cookies are puffed up, cracks form on the surface, and bottoms are lightly golden brown, about 7 to 9 minutes. Cool on the sheet pan for 5 minutes, then transfer to a wire rack to cook completely.
Make the Glaze - In a stand mixer or medium bowl, whisk the powdered sugar, lemon juice, and ¼ teaspoon anise extract. It should have a glue-like consistency. If needed, thin with a ¼ teaspoon of water at a time.
Decorate the Cookies - Working one cookie at a time, dip a little less than halfway into the glaze, shaking off the excess. Immediately add sprinkles before the glaze sets. Let them dry before serving for at least 30 minutes.
Notes
Shinier and Smoother Glaze: Add 2 teaspoons of light corn syrup. If needed, thin with a ¼ teaspoon of water at a time.
Storing: Store in an airtight container at room temperature for 5 days.
Freezing: Store in resealable plastic bags for up to 1 month. Transfer to a plate to defrost.