Preheat oven to 325°F/165°C, conventional or convection setting. Line a couple of cookie sheets or baking trays with silicon baking mats or silicon paper 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 light and creamy looking. The time this takes will vary depending on how soft your butter is to begin with, and how strong your mixer is.
1 cup unsalted butter, 3/4 cup superfine sugar, ½ teaspoon fine salt
While the butter and sugar are creaming, sieve the all-purpose/plain flour into a bowl.
2 cups all-purpose flour
Add the flour to the butter mixture in 2-3 batches, mixing on low speed just to combine each time. When all the flour has been added and the dough just comes together, turn it onto a lightly floured surface and knead lightly until it’s smooth. Don’t go overboard, you just want a cohesive mass that’s all the same color and consistency.
2 cups all-purpose flour
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 cut out larger shapes with a small cutout in the center of each one. If you're finding the dough is too soft to cut clean shapes, refrigerate it for 15 minutes before cutting.
Place the cut out shapes on lined trays, leaving ½”/1½ cm between each cookie. Use a teaspoon to transfer a small amount of crushed hard candy into the center cutout of each cookie. You need enough for it to fill the space, but don't pile it too high or it'll run and leak outside the edges of the cutout during baking. I prefer sticking with one color for each cutout; you can make multicolored stained glass but it tends to run and blend more than I like. Optional; brush a little beaten egg white or water on the outer border of the cookies and sprinkle with coarse sugar crystals.
3 Tbsp coarse sugar, 20 hard candies
Bake the stained glass 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.