Whisk together the flour, cornstarch and salt. Set aside
Using an electric mixer, beat the softened butter and powdered sugar to cream until nice and smooth. Add the vanilla and beat to combine.
Slowly add the dry ingredients into the wet and beat just until combined. Dough may be somewhat crumbly but not dry and should pull together to form a nice ball of dough.
This can technically be rolled into cookies and baked without chilling, but there will be a touch of spread. My suggestion is form two discs and chill for about 30 minutes at least, or up to about 2 hours for the really nice, no spread look. If chilling more than 2 hours, you can roll out into about ¼ inch to ½ inch thickness and chill between layers of parchment.
Once chilled, on a lightly floured surface, roll into ¼ to ½ inch thickness—the ½ inch makes for the soft, more melt in your mouth cookie and the thinner will be more of a crisp cookie that will snap in half.
Press egg cookie cutter to form the cookies and line a parchment lined baking sheet. Bake in oven preheated to 350° for about 8-12 minutes—based on thickness and how long chilled, the time will vary. I remove them as soon as a very slight golden color starts to show around the base edge of the cookies. Err on the side of under baking.
Allow the cookies to cool for several minutes and then transfer to cooling rack.
Once cooled, whisk the icing ingredients together and adjust to desired thickness. I add 3 drops arctic blue and 2 drops apple green (from chefmaster pastels food coloring)—just a nice light blue-ish with a light touch of green is great but you can aim for any color you like really!
Dip the top of each cookie into the icing and allow excess icing to fall off or spread with an offset spatula.
Stir the cocoa powder with the water and then use a pastry brush and lightly tap it over the iced cookies to make speckles. Allow to cool and set for several hours to allow to fully set.