Prep the oven and baking sheets. Preheat oven to 350°F with two racks spaced equally. Line two large baking sheets with parchment paper.
Cream the butter and sugar. In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using a handheld mixer, cream together the butter and sugar for 2-3 minutes or until well combined. Add the egg yolks and lemon zest and beat 1-2 minutes more until lightened in color and fluffy.
Add the dry ingredients. In a small mixing bowl, combine the salt and flour. Add it to the butter-sugar mixture, one cup at a time. Mix on low after each addition and stir just until the flour is combined.
Shape and fill the dough. Using a cookie scoop or a tablespoon, portion out the dough and roll into balls. Roll them smooth in your palms and place them onto the baking sheets one inch apart. Indent each ball of cookie dough using your thumb, or the handle of a large wooden spoon. Carefully place a small amount of lemon curd into each cookie.
Bake, cool, and glaze.. Bake at 350°F for 14-16 minutes or until the cookies are set. The bottoms and edges will be slightly golden brown. Let them cool on a wire rack. Mix up the powdered sugar and milk to make the glaze and drizzle over cookies. Store at room temperature for up to 3 days.