Add ½ cup (58g) of the walnuts to the food processor fitted with a blade attachment. Puree until the walnuts are finely ground.
Add the butter to the bowl of a stand mixer fitted with a paddle attachment. Beat the butter until light, about 1 minute. Scrape down the sides and add the sugar, beating until light and fluffy, about 2 minutes.
Slowly add the flour and mix to combine. Next, add the ground and chopped walnuts, lime zest, and salt, mixing once more.
Divide the dough between two bowls, cover and refrigerate to chill for at least 30 minutes and up to overnight.
Add the freeze dried strawberries and confectioners sugar to a food processor fitted with a blade attachment. Pulse until finely ground to the consistency of powdered sugar. Add to a large shallow bowl.
Heat oven to 325ºF (190ºC). Working with half the chilled dough at a time, scoop 1 tablespoon (20g) portions and roll into a ball, placing on a parchment paper-lined baking sheet.
Bake the cookies until golden brown on the bottom and pale, golden brown on top, about 18 to 20 minutes.
Let cool slightly for 5 minutes, then toss in the strawberry powdered sugar mixture.
Let cool completely on a cooling rack. Store in an airtight container for up to 4 days.