In a medium bowl, whisk together the flour, 1/2 cup confectioners' sugar, and kosher salt.
In a large bowl, beat together the butter, 1/4 cup confectioners' sugar, lemon zest, and lemon juice. Beat until light and fully combined, about 4-5 minutes. Beat in the flour mixture on low speed until just combined.
Next, roll the dough into 1-inch balls. Place the dough balls in the freezer for 12-15 minutes. Transfer, dough balls to a parchment paper- or silicone-lined baking sheet, making sure the dough balls are about 2 inches apart.
Bake for 10 minutes. Then, gently press the rounded part of a teaspoon or end of a wooden spoon handle into the center of each ball to create an indent. Continue to bake for 16-18 more minutes or until the cookies just start to brown on the bottom. Place the cookie sheets on a wire rack to cool.
While the cookies cool, make the glaze by whisking together the confectioners' sugar, lemon juice, and raspberries. (You can break up the raspberries with a fork to evenly distribute them in the glaze.)
Dust the cookies with confectioners' sugar. Then spoon or pipe the glaze into the indents. Let the cookies set for at least 10 minutes.