Preheat the oven to 350°F/180°C. Line a cookie sheet with parchment paper or silicone baking mats and set aside.
In a medium mixing bowl, whisk together flour and salt.
In a large mixing bowl using an electric hand mixer, or in the bowl of a stand mixer, add the softened butter and ⅔ cup of granulated sugar. Cream until light and fluffy. This takes about 3 minutes.
Add the lemon zest and vanilla and stir to combine. Then add the flour, a bit at a time, and mix until incorporated, scraping down the sides of the bowl to mix everything together.
Place the rest of the sugar in a small bowl. Use a cookie scoop to scoop 1.5 tablespoon sized dough balls, and roll each with your hands to smooth them. Roll each ball through the granulated sugar and place on sheet trays, leaving two inches between each cookie.
Make indentations in the cookies using the end of a round wooden spoon or similar tool. The indention should be about ⅔ of the way down into each ball. Don’t worry if the dough cracks on the edges; this is normal.
Fill each cookie with a heaping teaspoon of lemon curd.
Bake for 13-15 minutes or until the tops of the cookies look dry and the bottoms are lightly golden brown. Let the cookies cool on the tray for 5 minutes, then transfer to a wire rack to cool completely before adding the glaze.
To make the lemon glaze, mix together the lemon juice, powdered sugar and vanilla. Adjust the consistency if needed by adding a bit more juice or sugar. It should be thick, but pourable.
Glaze the cookies with the icing by dipping a fork into the glaze and drizzling it over the cookies while they are on the rack. Any excess will drip off. Give the glaze 15 minutes to set before serving or storing.