Preheat your oven to 350°F (175°C) and line two baking trays with parchment paper.
In a large bowl, cream together the softened butter and granulated sugar until the mixture is light and fluffy, about 3 minutes.
Add the egg yolk and vanilla extract to the butter mixture, beating until fully incorporated.
Gradually mix in the flour and salt on low speed until a soft dough forms; do not overwork the dough or the cookies will become tough.
Roll the dough into 1-inch balls and place them on the prepared baking trays, spacing them 2 inches apart.
Use your thumb or the back of a small measuring spoon to press a deep indentation into the center of each dough ball.
Bake for 12 to 14 minutes, or until the edges are just barely golden; if the indentations have puffed up, use the back of a spoon to gently press them down again while they are still warm.
Allow the cookies to cool on the tray for 5 minutes, then transfer them to a wire rack to cool completely.
Once the cookies are cool, spoon or pipe approximately 1/2 teaspoon of lemon curd into the center of each cookie.