Beat the butter, sugar, and lemon zest together in a large bowl until the mixture turns pale and fluffy, about 3 minutes.

Mix in the vanilla extract.

Add the flour and salt and mix just until the dough comes together; overmixing makes the cookies tough.

Shape the dough into a log about 2 inches thick, wrap it in plastic, and refrigerate at least 1 hour, until firm enough to slice cleanly.

Preheat the oven to 350 degrees F and line two baking sheets with parchment paper.

Slice the chilled log into rounds about 1/4 inch thick and space them 1 inch apart on the sheets.

Bake for 12 to 14 minutes, until the edges turn pale gold while the centers stay soft; they firm up as they cool.

Let the cookies cool on the sheet for 5 minutes, then move them to a wire rack to cool completely.

Dust the cooled cookies with powdered sugar just before arranging them on a platter.