In the bowl of a stand mixer with paddle attachment or in a large bowl with a hand mixer, beat butter, sugar, and salt on medium-high speed until light and fluffy, 3-5 minutes. Mix in raspberry and vanilla extract.
With mixer running on low speed, add flour and crushed freeze-dried raspberries to mixture and beat until just combined, taking care not to over-mix. Dough may be crumbly.
Using your hands to pull together, divide dough in half and place each half on large pieces of plastic wrap. Fold plastic wrap over dough to completely cover and use your hands to roll the dough into a smooth log, roughly 1 ½" in diameter. Repeat with second half of dough and then place in fridge to chill until firm, about 2 hours.
Preheat oven to 350 degrees and line two rimmed baking sheets with parchment paper. Taking one dough log out of the fridge at a time, brush the outside of each log with egg wash and roll in coarse sugar.
Slice each log into ½"-thick rounds and arrange on prepared baking sheet about 1" apart. Bake for 10-13 minutes, until edges are just beginning to turn golden. Let cool slightly on pan before moving to a cooling rack to cool completely before icing.
Dip cooled cookies in raspberry glaze, coating about ½ of cookie. Sprinkle on additional crushed freeze-dried raspberries. Let glaze harden before enjoying.