Preheat oven to 325°
In a medium bowl, mix together, butter, shortening, sugar and egg. Add vanilla, lemon extract and milk. Mix well until combined. Gradually stir in flour and baking powder scraping down the sides of bowl.
Roll out a small amount of dough on a floured surface to about 1/4″ thick and cut into shapes. Place on cookie sheets and bake until edges just start to brown. Approximately 10-12 minutes. Let sit on cookie sheets for a few minutes then transfer to cooling rack. Repeat until all dough is used.
In a large mixing bowl, whisk sugar and milk until smooth.
Add corn syrup and vanilla and whisk until well incorporated.
Divide frosting into separate bowls and add desired food coloring. Stir.
Spoon frosting into piping bags and outline each cookie, then fill it in and use a tooth pick to spread the frosting around to cover the area.
Once frosting hardens, add additional designs with leftover frosting.