In a bowl cream butter and sugar with electric mixer on low speed. Mix until almost all the sugar dissolved. Don't forget to scrape the sides of the bowl.
Add egg and mix thoroughly. Add vanilla extract and mix again.
Sift flour and salt. Add 1/4 of flour mixture to the butter mixture with low speed. Add every 1/4 of flour mixture until combined. Do not over mix.
Divide the sugar cookies dough into 2 pieces. Shape into rectangle and coat with plastic wrap. Place into the fridge for 30 minutes.
After 30 minutes, roll the dough between 2 parchment papers until the thickness is about 1/4 inch. Cut out cookie shapes. Place on the parchment paper-lined baking sheet. Place into the fridge for 30 minutes. Preheat oven to 350°F or 175°C.
Bake cookies for 8-12 minutes or until the edges become golden brown.
If you can't find pasteurized egg whites, you can follow this step: Bain Marie the egg whites, while heating whisk frequently until the egg whites hot to the touch. It should reach at least 140°F/60°C and no higher than 150°F/65,5°C.
In a bowl whisk the icing sugar and pasteurized egg whites with electric mixer. Add cream of tartar and clear vanilla extract. Add water and mix every 1 tbsp. Mix on slow speed for 10-15 minutes.
In small bowls divide the royal icing into several parts. Add gel food coloring of your choice.
Decorate: transfer icing to pastry bag and pipe as desired onto sugar cookies.