Preheat oven to 375 degrees F. Line a large baking sheet with parchment paper.
Place the melted and cooled shortening in a large mixing bowl and add the sugar and extract of choice. Use an electric mixer to combine it well. Add the eggs, one at a time, beating in between each addition.
In a medium mixing bowl, combine the flour, baking powder, and salt.
Gradually add the flour mixture to the wet mixture, beating to form a soft dough.
Using a small cookie scoop, shape the dough into neat 1 to 1 ½ tablespoon balls and place them about 1-inch apart on the prepared baking sheet.
Bake for 8 to 10 minutes (check after 8 minutes - tops will crack but stay light colored, bottoms should be golden). Transfer to a wire rack to cool. Cool before icing and decorating.
For the icing, add the powdered sugar, extract, and 2 tablespoons milk to a small bowl and stir until combined. Stir in additional milk, ¼ teaspoon at a time, until icing reaches the desired consistency. It should be thin enough to easily pour off the spoon, but not watery.
Once cooled, dip the cookies, top down into the icing. Shake off the excess and place the cookies down on the wire rack. Sprinkle with nonpareils or sprinkles and let them rest at room temperature to allow the icing to set up.