Preheat oven to 300°F/150°C, conventional setting (no steam!). Line a couple of cookie sheets or baking trays with parchment and set aside.
Put the butter, sugar and salt into the bowl of a stand mixer fitted with the paddle attachment and beat on medium speed until it's soft and creamy (you don't need to beat the butter until it's really fluffy, as this will make your cookies spread and be too delicate). The time this takes can vary depending on how soft your butter is, and how strong your mixer is. It takes 2-3 minutes in my KitchenAid.
1 cup unsalted butter, 3/4 cup superfine sugar, ½ tsp fine salt
While the butter and sugar are creaming, sieve the all-purpose/plain flour into a bowl.
2 1/2 cups all-purpose flour
Add 3/4 of the flour to the butter mixture, mixing on low speed to combine. You're looking for a soft but cohesive mass; not too crumbly but not greasy and squishy either. If needed, add the last 1/4 of the flour a spoonful at a time until you get the right consistency.
2 1/2 cups all-purpose flour
When the flour has been added and the dough just comes together, turn it onto a lightly floured surface and knead lightly just until it’s smooth.
For cut-out cookies or stamped cookies, roll portions of dough out between two sheets of parchment paper to your desired thickness. I like larger shapes to be about 3/8"/1cm thick and smaller shapes 1/2"/6mm thick. Remove the top sheet of parchment and either cut out or stamp cookies. If you're finding the dough is too soft to cut clean shapes, refrigerate it for 15 minutes before cutting.
Place cut out shapes on lined trays, leaving ½”/1½ cm between each cookie. If you want traditional Danish-style butter cookies, brush a little egg wash or water on the cookies and sprinkle with coarse sugar crystals.
3 Tbsp coarse sugar
Bake the butter cookies until firm to the touch and just beginning to color at the edges. This can take anywhere from 15-25 minutes, depending on their size.
Cool the cookies on the baking trays for 5 minutes, then transfer to a cooling rack. When completely cool, store in an airtight container. If you haven't sprinkled them with sugar, these cookies can be decorated with royal icing or fondant.