Preheat your oven to 350 degrees, and line two large baking sheets with parchment paper. Set aside.

In a large mixing bowl, beat together the butter and sugar until light and fluffy. This will be a little more work than normal because of the cold butter, and I recommend using a stand mixer or an electric hand mixer. Doing it by hand will be difficult.

Beat in the vanilla extract and eggs until combined. Add in the flour and salt, and beat until a dough forms. It will be fairly firm, and you want to beat it for several minutes to ensure that all the flour is completely incorporated.

Take about half of the dough, and form it into a ball on a sheet of parchment paper. Place the other half of the dough into the fridge (in the mixing bowl is fine). Place another piece of parchment paper on top of your dough and roll out the dough until it is about 1/4 inch thick. Place the whole rolled out dough sheet into the fridge for about 20 minutes, or until very firm. Cut out into your desired shapes and place the cut cookies onto your prepared pans. These don't spread while baking, so you can place them pretty close together.

Bake cookies for 8-10 minutes, or until they are just starting to become golden on the edges if you want them to stay soft, and 12-14 minutes or until golden brown on the edges if you want the cookies crisp. Continue with the remaining dough until all the cookies are baked. Cool completely before decorating with your royal icing and sprinkles!

In a large bowl, whisk the egg whites and vanilla extract until the egg whites are lightly frothy. Add in the powdered sugar and salt, and whisk until you have a thick icing. Depending on the consistency you want, you can adjust by adding more powdered sugar, or a little bit of water! Ice your cookies as desired, and top with sprinkles. Let the icing set without covering for 1-2 hours, and then store the iced cookies in an air-tight container and enjoy!