In a bowl of a stand mixer with a paddle attachment, beat together butter, vanilla, and powdered sugar until light and creamy. On medium speed for about 5 minutes. Scrape the bowl a few times during the process.
In a separate bowl, whisk together all-purpose flour and salt, then turn the mixer to its lowest speed and gradually add the dry ingredients to the butter mixture.
Use a spatula to fold in all of the pistachios.
Transfer the firm yet pliable dough onto a large sheet of parchment paper. Roll the dough into a 10” log, about 2 inches thick. Wrap the dough in parchment paper and refrigerate for about 3 hours or overnight.
Once the dough is firm, cut the log into ¼” rounds. Place cookies onto the baking sheet lined with parchment paper about 1 inch apart. Bake at 350 degrees F for about 13-15 minutes or until lightly golden on the edge.
Let cool on the baking sheet for a few minutes, and then transfer to the cooling rack to cool completely.
Melt the chocolate using a microwave or double boiler.
Dip cookies into the melted chocolate and place them on the parchment paper to set. If desired, sprinkle with extra chopped pistachios and coarse salt or salt flakes.