In a stand mixer (using the paddle attachment) or with a handheld mixer, beat the softened butter on high speed for about 1 minute until smooth. Add sugar and vanilla extract, and beat until light and fluffy for about 1-2 minutes. Decrease to medium speed, and mix in the salt and flour until evenly incorporated. Add the pistachios and mix a few more times on low speed until evenly incorporated.
Divide up the dough into two equal parts. Transfer each dough onto plastic wrap and roll into 2.5 inch diameter logs. Wrap tightly, twisting the ends (see picture above). You should have two logs. Refrigerate them for at least 3 hours or overnight.
When ready to bake, preheat oven to 325 degrees F. Line 2 sheet pans with parchment paper.
Slice cookies into 1/3 inch thick slices, and place them on prepared sheet pans. Make sure they stay cold so that they retain their shape in the oven. Bake for about 18-20 minutes or until slightly golden on the edges. They will look soft, but will harden as they cool down.
Remove from oven and let them cool on the pan for a 5 minutes or so. After they are manageable, transfer them to a cooling rack and let them cool completely.
Once the cookies have cooled, melt the chocolate in the microwave oven, checking and stirring every 10-15 seconds. Dip cookies halfway through into the melted chocolate, and place on a lined sheet pan. Sprinkle with the pistachio bits and some sea salt if desired. Let them cool until the chocolate hardens. Enjoy!