Add butter and sugar to a large bowl (or the bowl of a stand mixer). Beat until it's soft and creamy — about 4 minutes to medium speed. You can go as long as 8 minutes here, since the creamier the mixture, the better. Add egg and vanilla and mix until just combined.
In another bowl, whisk together all the dry ingredients: flour, salt, and baking soda.
Slowly add the flour to the creamed butter-sugar mix (~¼ cup at a time) and beat until it's completely incorporated, but don't overmix the dough. The dough should be smooth and sticky (similar to play doh).
Split the dough into two parts. Transfer both parts to a flat surface, cover it with plastic wrap or place them between two large sheets of parchment paper and flatten the dough using your hands and a kitchen dough roller.
Refrigerate for at least 5 hours and up to 2 days. I typically like to chill it overnight. This allows the cookies to not spread too much and keep crisp edges when you bake them.
Once chilled, preheat the oven to 350°F and line two or three baking sheets with parchment paper.
Remove the paper wrap and use Christmas themed cookie cutters to cut the dough (If the dough is too sticky to work with, take the dough to the fridge five minutes before cutting it). Dip the cookie cutters in some flour to make this process easier.
Bake for about 8 minutes or just until the edges are golden brown. You don't want to overbake the cookies!
Let them cool for at least 10 minutes before removing them to a cooling rack. (they could break when still warm).
Make Icing
In a medium bowl, combine the sifted powdered sugar with 2 egg whites and mix with a fork until incorporated. The egg whites add flavor and help ensure consistency.
Add lemon juice and mix on low speed with a stand mixer for five minutes until firm peaks are formed.
Separate the mixture into different small bowls for each color. Add 1 drop of coloring gel to each bowl and mix until the desired color is uniform. I used red, white and green to keep up with Christmas colors, but the sky is your limit!
Cover the bowl with plastic wrap to avoid the icing dries out.
Decorate the cookies
After ensuring that the cookies are completely cool, place the icing in a piping bag, ziplock bag, or squeeze bottle. If using a bag (like shown in the pictures in my post), make a small hole in the edge. Using a squeeze bottle will likely be much easier!
Decorate the cookies as you desire.
Allow the icing to dry completely (about 3 hours minimum, ideally overnight again) before serving. This is especially important if you plan to wrap the cookies or create treat bags!
Notes
Use room temperature (high quality) ingredients, especially butter.
Don't overmix the sugar cookie dough. Once all of your ingredients are just combined, stop mixing!
Roll out your dough before chilling! Use either a really non-stick baking sheet (like this one!) or roll dough between sheets of parchment paper so you don't need to keep dusting the surface all the time!
Let the cookies rest. The colder your cookie dough is when it goes into the oven, the better chance you have of getting those perfect shapes and crispy edges we all love in our sugar cookies!
Use gel food coloring. Liquid food coloring can thin out your royal icing too much, making it difficult to pipe onto the cookie surface without creating a mess.
Make sure the icing is the right consistency. Royal icing should be slightly runny but still thick enough that it won't just run off of the sides of your cooled cookies when piped or spread on top. Too thin and you won't have enough structure; too thick and you won't be able get nice details when decorating.
Add powdered sugar or water to get the right consistency before adding any food coloring or flavoring extracts. If you want to add Christmas sprinkles, do it before the icing dries out.
Make sure the cookies are completely chilled before decorating. If they are completely cool, the icing will melt.
Use a squeeze bottle to ice the cookies. I've found them to be way easier to handle than piping tips, and this is a great way to get the kids involved! These ones are my favorite because they come in different sizes!
Allow at least 24 hours for the icing to set. This is important if you plan to make treat bags with cookies in order to avoid cookies sticking to each other.