In a heatproof bowl, combine caster sugar and cornstarch, whisking well to eliminate lumps. Incorporate egg, lemon juice, and lemon peel until smooth. Place over a simmering pot of water, cooking for about 10 minutes while stirring until thick. Mix in butter and let cool. Chill for at least 30 minutes, freeze portions for 1 hour.

In a large bowl, cream the butter and caster sugar until fluffy. Add lemon zest and vanilla, mix thoroughly, then blend in egg until combined. In another bowl, sift flour, salt, and baking soda, then fold dry ingredients into wet mixture to create a non-sticky dough. Chill dough for 20 minutes.

Preheat oven to 350°F (180°C) and line a baking tray with parchment. Take a scoop of chilled dough, flatten it, place frozen lemon curd in the center, fold dough around the curd, and shape into a ball. Roll in granulated sugar, place on tray with space between cookies.

Bake for 8-9 minutes until edges are golden and centers remain soft and slightly puffed. Cool on tray for a few minutes before transferring to a wire rack to cool completely.