Preheat your oven to 450°F (232°C). Line a baking sheet with parchment paper and set it aside.
To a medium mixing bowl, add the butter, powdered sugar, lemon zest, and lemon juice. Using a hand-held electric mixer, beat the ingredients until combined and smooth, about 2-3 minutes.
Add the flour and salt to the bowl and beat into the butter mixture until the dough comes together. The dough will be very sandy and crumbly at first, then will start to come together more. Beat the dough for about 3-5 minutes, until you are able to press it into a ball with your hands.
Using a 1 ½ tablespoon cookie scoop, scoop out cookie dough, pressing against the side of the bowl while scooping to level the scoops and pack the dough into the scoop. Scoop the dough ball into the palm of one hand and roll the cookie between both palms to form a round ball.
Place the balls on the prepared cookie sheet, spacing them about an inch and a half apart. Dip the back of a ½ cup measuring cup in flour and use it to press the cookies into flat discs about ¼ inch thick. The flour helps the cookies not stick to the measuring cup.
Bake the cookies in the preheated oven for 7-10 minutes, or until the tops are no longer glossy. Do not brown the cookies! Allow the cookies to cool on the baking sheet for 5 minutes then transfer them to a wire rack to cool completely.
While the cookies are cooling, make the strawberry glaze. Pulse the freeze-dried strawberries in a food processor until they are almost a fine powder. You should get about 2 tablespooonsof powder. Transfer the strawberries to a small mixing bowl along with the powdered sugar, vanilla extract, and one tablespoon of milk or half and half.
Using a small whisk, mix the ingredients together until smooth. Add more milk if needed until the glaze can be drizzled with a spoon but is not thin enough to run off the sides of the cookies.
Spoon about ½ teaspoon of glaze onto the completely cooled cookies, one at a time, and smooth out into an even layer with the back of the spoon. Leave a small rim around the perimeter of each cookie. Top the glazed cookies with fresh lemon zest if desired. You can allow the glaze to set for a few minutes, or enjoy the cookies immediately!