Preheat oven at 190°C/370°F. Grease and flour a baking sheet.
Beat butter and sugar. Add the lemon zest, egg, milk and vanilla extract.
Sift together flour, baking powder and salt, and add to the mixture. Knead just until the dough comes together.
Dust the work surface with flour, roll out the dough and cut out shapes with cookie cutters. Bake for 10-12 minutes. Let them cool completely.
For the frosting: Mix together powdered sugar and water to obtain the desired consistency. If it is too thick, add a few drops of water to thin it out, and if it is too runny, add some more confectioners' sugar. Then add a few drops of food coloring and mix well. Add some sprinkles.
