Add the butter and sugar to a large mixing bowl and cream the butter and sugar until light in color and fluffy.
Beat in the egg and vanilla until light and fluffy.
Add the flour, salt, lemon zest, and thyme leaves and mix until well combined. Don't overmix.
Cover the bowl with cling wrap and rest in the refrigerator for 1 hour or more.
Preheat the oven to 180°C, after the dough has rested.
Remove the dough from the refrigerator and remove half of it from the bowl. Place the other half of dough back in the refrigerator.
Liberally dust a clean surface and rolling pin with flour.
roll out the dough 8ml thick and use a glass or cookie cutter to cut out circles in the dough. Roll scraps together and roll out again, repeating the process until all the dough has been rolled out and cut into circles. Remove the other half of the dough from the refrigerator and continue to roll out and cut out circles as explained above.
Place the dough circles on a baking sheet lined with baking paper and place into the preheated oven.
Bake the cookies for 8-10 min until they are slightly golden in color. Remove from the oven and let it rest for five minutes before transferring to a wired rack to further cool down.
Give the cookies sufficient time to cool down completely before decorating with lemon drizzle icing.