LEMON CURD: Make the lemon curd at least one day in advance. To make the lemon curd: combine 1 and 1/2 cups sugar and lemon zest (zest of 3 lemons, about 3 tablespoons) in a food processor. Pulse 15-20 times and then pour into a medium-sized bowl. Add the room- temperature butter to that bowl and using a hand mixer, beat until light and creamy-- about 3-4 minutes. Beat in the eggs one at a time, mixing well between each addition. Add in the salt and 1/2 cup freshly squeezed lemon juice. Beat to combine.
LEMON CURD CONT.: Pour the mixture into a medium-sized saucepan and place over low heat. Stir constantly for about 10 minutes or until thickened. The curd must reach 170 degrees on a candy thermometer. (If it doesn't reach this heat, it won't properly set up). Pour curd through a fine mesh sieve and use a spatula to press it through the sieve into an airtight container. Place plastic wrap right on top of the curd (so the plastic wrap is touching the lemon curd; this keeps the lemon curd from developing a film) and cover the container with a lid. Refrigerate 8 hours or overnight before using. Lemon curd will stay fresh for 5-7 days in the fridge.
COOKIES: In a large bowl, add the room-temperature butter and sugar. Beat at medium speed until smooth and creamy, scraping the sides as needed. Add the almond, vanilla extract, cornstarch, and salt and mix until combined. Add flour to the bowl. Beat together at low speed, scraping bowl as needed, until all ingredients are combined. Do not over-mix the dough.
CHILL COOKIES: Shape the cookies into small balls -- the size of 1 tablespoon (using a tablespoon measuring spoon to form and measure balls) and then roll the cookie dough balls in the 1/2 cup granulated sugar until generously coated. Next, gently indent the center of each cookie dough ball with your finger. Place these cookies 2 inches apart on a Silpat or parchment paper-lined baking sheet. Cover and refrigerate for 1 hour (or freeze for 30 minutes). Remove from the fridge and add completely chilled and thickened lemon curd to fill (but not over fill) the centers of all the cookies. Return the cookies to the fridge for 10 more minutes.
BAKE: Preheat the oven to 350 degrees F. Bake the cookies for 8-10 minutes or until very lightly browned and the tops are no longer glossy (slightly under bake for soft and delicious shortbread cookies).
COOL COOKIES: Remove cookies to a cooling rack and allow them to cool completely. Meanwhile, prepare the glaze by whisking all the ingredients together in a bowl until smooth. (Add heavy whipping cream or milk until you've reached your desired consistency; I like the glaze on the thicker side, but you may want to add a bit more cream or milk).
GLAZE: Drizzle the glaze over the cookies (either drizzle with a spoon or transfer the glaze to a plastic bag and cut off the tip to pipe). Allow the glaze to set. Cookies are best enjoyed within 3-4 days; store in an airtight container at room temperature.