In a stand mixer (using the paddle attachment) or with a handheld electric mixer, beat the softened butter on medium-high speed for about 1 minute until smooth. Add sugar and continue beating until light and fluffy, another 1 to 2 minutes, scraping the sides of the bowl as needed.
Decrease to medium-low speed, and mix the vanilla extract. Then, gradually add the flour and salt, mixing until fully incorporated. Mix in the chopped pistachios until evenly combined. Do not overmix. Note: The dough will look a bit crumbly first, but will come together into a more uniform dough as you mix it. You can also use your hands to incorporate as needed. It should not crumbly or sticky.
Divide up the dough into two equal parts. Transfer each dough onto plastic wrap and roll into about 2.5 inch diameter logs, minimizing flat or squished edges. Wrap tightly, twisting the ends. Refrigerate for at least 3 hours or up to 3 days. Tip: Make the logs a bit thicker first so you can roll and shape them out to the desired size.
When ready to bake, preheat oven to 325 degrees F. Line 2 sheet pans with parchment paper.
Slice cookies into ¼ inch thick slices, and place them on prepared sheet pans about 2 inches apart. Make sure they stay cold so that they retain their shape in the oven. Tip: If the logs are too hard to cut, let them sit on the counter for 10 minutes.
Bake for about 16 to 18 minutes or until slightly golden brown on the edges. They will look soft, but will set as they cool down. Remove from oven and let them cool on the pan for 5 minutes or so. Then, transfer to a cooling rack and let them cool completely.
To decorate, melt the chocolate in the microwave oven, checking and stirring every 20 seconds until smooth and melted. Dip cookies halfway through into the melted chocolate and place on a lined sheet pan. Immediately sprinkle the pistachio bits and some sea salt on top of the chocolate so they stick. Let cool until the chocolate sets or refrigerate for 15-20 minutes to allow the chocolate to set better and faster. Enjoy!