Soften your butter, you don't want to melt it, but it can also not be rock hard, soften it like you would butter so that it is spreadable. (I pop mine in the microwave for a little while on low power).
Sift the free-from-gluten flour and baking powder into a small/medium bowl. If you don't have a sifter or sieve, you can pop the flour and baking powder in a bowl and whisk or fork it to remove lumps and ensure the baking powder is evenly distributed.
In a medium bowl (one large enough to eventually hold all the ingredients). Beat the butter, and caster sugar until well combined, thick and creamy.
Add the egg, vanilla, salt and vinegar, beat until well combined.
Gradually add the flour to the wet ingredients, beating on low speed until all the ingredients are combined. Be sure to scrape the sides and bottom of the bowl to get all the ingredients into the dough.
Cover the dough and refrigerate for 30 mins
Preheat your oven to 160 degrees celsius
Roll out the dough to the thickness you want. The thickness will affect baking time, mine are typically 4-5mm thick. (I roll mine out on a piece of baking paper. Use cookie cutters to make any shape you want. Lay the cookies out on a baking paper-lined cookie tray and chill again.
Bake your cookies for 10-12 minutes, until they are just firm and lightly golden on the edges and the bottom. (they won't colour very much)
Allow to cool fully before icing.