Position a rack in center of the oven and preheat to 325°F. Line a large baking sheet with parchment paper.
Whisk flour, baking powder, and salt in medium bowl and set aside. In a large bowl using an hand mixer or in a stand mixer fitted with the paddle attachment, beat butter and sugar until smooth. Add 1/2 cup pistachios and vanilla. Beat in flour mixture until just combined.
Shape tablespoonfuls of dough into logs about 3 inches long. Place on baking sheet, leaving about 1 inch of room between each cookie. Bake until golden brown around edges, 18-20 minutes. Cool completely.
Put chopped chocolate in a double boiler set over barely-simmering water. Stir chocolate until melted and smooth, about 5 minutes. Remove from heat. Place remaining 1/3 cup pistachios in a small shallow bowl. Dip one end of each cookie in the melted chocolate about 1-1 1/2 inches deep. Let excess chocolate drip back into bowl, then roll chocolate-coated end in chopped pistachios. Repeat with the rest of the cookies. Let stand until chocolate has hardened, at least one hour. Cookies will keep in airtight container up to 1 week.
This recipe yields 1 1/2 dozen cookies and can easily be doubled.
Recipe by About a Mom at https://www.aboutamom.com/chocolate-dunked-pistachio-shortbread-cookies/