Prep. Preheat the oven to 320°F. Line baking sheets with parchment paper or silicone baking mats and set aside.
Combine the dry ingredients. In a medium bowl, whisk together the all-purpose flour, baking powder, and salt until well combined. Set aside.
Cream the butter and sugar. In a large mixing bowl, beat the softened butter and granulated sugar until light and fluffy, about 2-3 minutes. This can be done using a hand mixer or a stand mixer with a paddle attachment.
Add eggs, lemon juice, lemon zest, and vanilla. Add the eggs, one at a time, beating well after each addition. Stir in the lemon juice, grated lemon zest, and vanilla extract, mixing until fully combined.
Mix in the dry ingredients. Gradually add the dry flour mixture to the wet ingredients, mixing on low speed until a soft dough forms. Be careful not to overmix.
Shape the cookies. Using a cookie scoop or a tablespoon, scoop the dough into small rounds and place them on the prepared baking sheets, spacing them about 2 inches apart.
Bake the cookies. Bake in the preheated oven for 10-12 minutes, or until the cookies are lightly golden around the edges but still soft in the center. Remove from the oven and allow the cookies to cool completely on wire racks.
Make the icing. In a small bowl, whisk together the confectioners' sugar and lemon juice until smooth. The icing should be thick but pourable; if needed, adjust the consistency by adding more lemon juice or sugar.
Cool the cookies and dip them in the icing. Once the cookies are completely cooled, dip the tops of each cookie into the lemon icing. If desired, sprinkle with colorful sprinkles while the icing is still wet. Allow the icing to set before serving or storing. Enjoy these Anginetti cookies with a cup of tea or coffee!