Heat the oven to 175 C / 350 F. Line two baking sheets with parchment paper.

Add the sifted powdered sugar and cold butter cubes to a large bowl. Rub together with your fingertips or mix on low speed until the mixture looks like coarse, clumpy crumbs.

Add the lemon zest and chopped thyme directly to the butter mixture. Mix until fragrant, about 30 seconds.

Add the egg yolk, vanilla extract, and fine salt. Mix until the dough just comes together into a smooth, non-sticky ball. If the dough feels crumbly, press it firmly with your hands until it holds.

Add the flour all at once. Mix on low or stir with a wooden spoon until no dry streaks remain. Do not overwork the dough.

Turn the dough out onto a lightly floured surface and roll to an even 6 mm thickness.

Cut out rounds with a 5 cm cutter and transfer to the prepared baking sheets, spacing about 3 cm apart. Gather scraps, re-roll once, and cut again.

Press a pinch of flaky sea salt onto each cookie if using. Bake for 12 to 14 minutes, rotating the pan at the 7-minute mark, until the edges are just golden and the centers still look pale.

Cool on the baking sheet for 5 minutes, then transfer to a wire rack. They firm up as they cool.