To prepare the sugar eggs, combine powdered egg whites and water in the bowl of a standing electric mixer. Whisk until all the powdered egg white dissolves and the mixture is frothy and well combined. Add food coloring, if using, and mix well. Add sugars and stir on low speed with the paddle attachment until the mixture is evenly mixed. Its consistency should feel like slightly damp brown sugar.
Press mixture firmly into the molds. Level the tops with the back side of a knife. Invert eggs on a baking sheet lined with parchment paper. Remove molds.
Heat egg halves in an oven preheated to 200º F for 15 minutes. Remove and cool to room temperature before hollowing the centers with a spoon (a grapefruit spoon works really well). Return the leftover sugar to the mixing bowl. Beat on low speed with the paddle attachment to break up any clumps. Add water, a little bit at a time while, until the mixture returns to a damp brown sugar-like consistency. Repeat molding and heating process.
Using a sharp knife or a hack saw, cut of the tips of the hollowed eggs to create the peek-a-boo openings. After trimming one half of an egg, line it up with its mate and mark a cut line to help you create an evenly shaped hole.
Prepare the royal icing for decorating the eggs. In the bowl of a standing electric mixer with the whisk attachment, mix together powdered egg whites and confectioner's sugar on low speed. Add water, mix slowly to combine, and then beat on high speed until stiff peaks form. Divide the icing into bowls and mix in food coloring as desired.
Pipe icing inside eggs and add decorations, inserting them into the frosting to help them adhere.
Pipe a thin line of royal icing around the rims of the eggs and set tops on the eggs carefully. Pipe decoratively around the seams and add other decorations as desired.