In a mixer, beat together the butter, then add in the sugar.Mix in the eggs and vanilla extract next.Then add in the flour, baking soda and salt.Set aside a bit (tennis ball size) for the checkerboard cookies.Roll the rest into cling wrap, and refrigerate for 1 hour.Once chilled, preheat your oven to 175C or 350F.Bring out the dough, and take off another tennis ball size of dough for the checkerboard cookies.With the rest, roll to about 1 cm thick and cut out the shapes.Bake for 8-10 minutes until golden brown.The first tennis ball sized dough you've set aside for the checkerboard cookies, place back in the mixer, and add in 2 heaped tsp of cocoa powder. Mix until combined.Wrap in cling wrap and refrigerate for 1 hour.When chilled, roll out both the chocolate and light coloured dough until 1 inch thick.Cut into long strips, where the ends look square.Whisk together the egg and water to create an egg wash.Wipe down the edges of the dough with the egg wash, and alternate the dark and light dough strips, pressing them together. So on the bottom layer, alternate- light, dark, light. On the next layer- dark, light, dark. On the top layer-light, dark, light. You can continue to make more of a rectangle if you wish.You should have a square ended rectangular box.Slice the cookie dough through so you cut off cookies that show the checkerboard pattern.Bake for 8-10 minutes.Whisk your egg whites in a mixer with the lemon juice.Then add in your sifted icing sugar. You'll want to start with a thicker icing so you can pipe your edges first.Once mixed, scoop them into individual bowls, and add the colours you want.Take small piping bags, and scoop part of the icing into their own bags.Snip off the top and edge the cooled sugar cookies. Let dry for a bit.Keep the icing in the bags, as you'll need the same consistency for the final decorating.To the additional royal icing in the individual bowls, add in a tsp of milk to each, and mix to make the icing smoother and runnier.Using either a piping bag or a small spoon, pour and help manoeuvre the icing so the cookie is flooded within the edges you've piped.Let dry.Finish off with piping extra designs on top.Let dry completely before serving.