In a large bowl, combine butter and sugar and use an electric mixer to beat until creamy and smooth, about 3 minutes.
Add egg and vanilla extract and beat until completely combined.
In a separate, medium-sized bowl, whisk together flour, baking powder, and salt.
Gradually add dry ingredients into wet until completely combined.
Divide the dough into 2 equal portions. Generously dust two sheets of parchment paper with flour and place one dough portion between the two sheets. Roll out to 1/4-inch thickness. Repeat with the remaining portion of dough. Place the two sheets of dough on a baking sheet and chill for at least 1 hour or up to 1 day. You can also freeze for 30 minutes.
Once dough has finished chilling, preheat oven to 350 F and line a baking sheet with parchment paper. Set aside.
Remove the dough from the fridge and cut into shapes with a cookie cutter, rerolling any scraps and cutting more shapes. Transfer the shapes to the prepared baking sheets. If the dough is too warm, freeze for 15 minutes or until firmed again.
Bake for 10 minutes, or until the cookies are set and begin to brown. Be careful not to over-bake. Let the cookies cool for 5 minutes before removing to a wire rack to cool completely.
For the Border Icing:
In a small bowl, use a fork to beat together all the ingredients except the food coloring. Beat in the food coloring, a few drops at a time, until colored to your liking. The mixture should be very thick but still pourable. Add more powdered sugar or water as needed.
Transfer frosting to a squeeze bottle or into a pastry bag fitted with a small plain tip.
Pipe frosting directly over one corner of a cookie, begin tracing an outline of the cookie, squeezing gently and using both hands if needed to maintain consistent pressure. If you mess up, simply wipe the icing off and start again. Allow the icing to dry slightly before continuing with the flood icing.
For the Flood Icing:
In a small bowl, use a fork to beat together all the ingredients except the food coloring. Beat in the food coloring, a few drops at a time, until colored to your liking. The mixture should still be pretty thick, but will drizzle more freely than the border icing. If needed, add additional water or milk to loosen until the consistency is pourable. Pour the flood icing into a squeeze bottle or into a pastry bag fitted with a small plain tip.
Begin filling the interior of the border drawn on each cookie with the flood icing, being careful not to add too much that it overflows the border icing. Use either the nose of the bottle or a small toothpick to push the icing evenly over the cookie and up against the corners.
Leave the iced cookie to dry for 24 hours. The cookies are dry when the surface is completely smooth, dry, and resists smudging when touched. Store the dried cookies between sheets of parchment paper in an airtight container at room temperature for up to 10 days.