In a large bowl beat the butter and sugar until fluffy - about 2 minutes.
Add vanilla extract, and then mix in the eggs one at a time.
In a separate bowl whisk together the flour, cornstarch, baking powder & salt.
With the mixer on low speed, beat the flour mixture into the butter mixture about 1/2 at a time.
Divide the dough into two equal pieces. Form each part into a round, flat disc shape and wrap each in plastic wrap.
Refrigerate for at least 2 hours.
When ready to bake, preheat the oven to 350F degrees and line cookie sheets with parchment paper. Take one disc of dough out of the fridge and let it warm up for 10 minutes.
Flour a clean work surface, and flour your rolling pin. Unwrap the dough and lightly dust both sides with flour.
Roll out the dough to about 3-5mm thick, or about 1/8 - 1/4 inch thick. Cut into egg shapes using cookie cutters and carefully transfer to the lined cookie sheets.
Bake one cookie sheet at a time for 8-10 minutes on the middle rack, or until the tops look just set. Remove from the oven and cool completely on wire racks, about 1 hour.
Repeat the process with the rest of the dough.
Sift powdered sugar into a medium bowl. Add 6 teaspoons of milk, corn syrup, and extract. Stir vigorously until icing is smooth.
If needed, add additional milk (1 teaspoon at a time) to thin icing more. You've reached the correct consistency for frosting if a scoop of icing slowly falls off the spoon. If your icing gets too thin, whisk in a little more powdered sugar as needed.
If making colored icing, divide into bowls and add food coloring. Add 1-2 drops of food coloring to each bowl and mix. You want nice pastel colors. Add more coloring as needed until your desired colors are achieved.
Transfer icing to piping bags and decorate your Easter egg cookies. Pipe the icing as an outline and fill in with more icing for pristine edges. Alternatively, it can also be spread with a small knife and decorated with sprinkles. This frosting hardens quickly so have sprinkles ready to put on immediately.
Before stacking or wrapping cookies, make sure the icing is completely hard. Set cookies on a baking sheet or wire cooling rack for 12 hours until icing is completely set.
Recipe yield varies based on the size of your cookie cutters.
If you find the cookies are spreading, after cutting into shapes and placing them on a cookie tray - refrigerate for an extra 10-15 minutes before baking.
Traditionally sugar cookie icing is flavored with almond or vanilla extract, but orange, lemon, maple, or coconut extracts can also be substituted.