Combine 2/3 cup of the shelled pistachios and 2 teaspoons of flour in a food processor, and pulse repeatedly until finely ground. Set aside.
For the cookies: Preheat the oven to 350 degrees F. Line two large baking sheets with parchment paper (or a silicone baking sheet). Whisk together the pistachio flour, remaining 1 cup all-purpose flour and salt in a medium bowl and set aside.
Combine the softened butter and granulated sugar in the bowl of a stand mixer fitted with a paddle attachment. Beat the butter and sugar on medium-high speed until light and fluffy, 3 to 4 minutes. Add the vanilla extract and mix thoroughly. Reduce the speed to low and slowly add the flour mixture, scraping down the sides of the bowl once or twice until the dough comes together and the dry ingredients are fully incorporated.
In a separate bowl, whisk the egg white until lightly frothy. Place the remaining 2/3 cup shelled pistachios in the same food processor bowl, and pulse until coarsely chopped. Place the pistachios in a small bowl.
Using your fingertips, roll the cookie dough into 1-inch diameter balls (about 1 tablespoonful). Dip each ball lightly into the egg white, and then roll the balls lightly in the crushed pistachios until coated evenly. Place the balls 2 inches apart on the baking sheets (roughly 12 cookies per sheet). Holding the cookie balls steady with one hand, poke a hole into the center of each cookie with the end of a wooden spoon, pushing down until just before you reach the baking sheet. Re-shape each cookie into a circle with your fingertips as necessary.
Bake the cookies, rotating the sheets halfway through the baking time, until the bottoms of the cookies are lightly golden, 16 to 18 minutes. Allow the cookies to cool on the baking sheets for 3 to 4 minutes before transferring them to a cooling rack to cool. Using a fine-meshed sieve, dust the cookies with confectioners' sugar.
In a small saucepan, heat the black currant jam until it reaches a boil. Remove the jam from the heat and spoon 1/2 to 1 teaspoon of jam into the center of each cookie. Allow the jam to cool and set completely.
The cookies can be stored in an airtight container for up to 3 days.