A homemade pistachio paste is the key element to the wonderful nutty flavor complementing the chocolate cookie. Of course, the pistachio coating adds even more to the flavor, while also adding a bit of crunch.
In a medium bowl whisk together flour, cocoa powder, 1 teaspoon salt, the baking powder, and baking soda.
In a large bowl beat brown sugar, 3/4 cup butter, 1/4 cup granulated sugar, the oil, and vanilla 2 minutes on medium or until well-combined. Add 1 egg and egg yolk; beat on low until combined.
Add flour mixture. Beat on low until some streaks of flour remain. Stir by hand until combined. (Dough will be sticky.) Chill, covered, 2 to 24 hours.
For pistachio paste: In a food processor combine 1 cup pistachios and remaining 1/4 cup granulated sugar. Pulse until finely chopped. Add 2 tablespoons water, remaining 1 tablespoon butter and egg, the almond extract, and remaining 1/8 teaspoon salt. Pulse until a thick paste forms. Add a few drops of green food coloring. Pulse to combine. Transfer to a bowl. Chill, covered, 30 minutes.
Roll out half the chilled dough to a 10x8-inch rectangle between two sheets of parchment paper sprinkled with cocoa powder; repeat with the other half of the dough. Chill 15 to 30 minutes or until just firm.
Remove top sheet of parchment from one sheet of dough. Spread with half the pistachio paste, leaving a 1/2-inch border. Tightly roll up dough, starting from a long side, using parchment paper to help. (If dough sticks, use a thin metal spatula to scrape dough away from the paper.) Repeat with remaining dough and pistachio paste. Chill, covered, overnight. (Roll the logs occasionally to help keep their shape.)
Preheat oven to 350°F. Line a cookie sheet with parchment paper. Finely chop remaining pistachios; place in a small bowl. Place milk in another small bowl. Using a sharp knife, cut logs into 1/2-inch thick slices. Roll edge of each slice in milk, then pistachios. Place slices 2 inches apart on prepared sheet. Bake 11 to 13 minutes or until edges are firm. Let cool on a wire rack. Store in an airtight container at room temperature up to 3 days. Makes 38 cookies.