Whisk the flour, baking powder and 1/4 teaspoon salt in a medium bowl. Beat 6 tablespoons butter and 1/3 cup sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Beat in 1 egg and the vanilla (don?t worry if the mixture looks separated). Reduce the mixer speed to low; mix in the flour mixture until combined. Turn out the dough onto a piece of plastic wrap; shape into a disk. Wrap and refrigerate until firm, about 1 hour.
Meanwhile, make the filling: Pulse the pistachios and remaining 1/3 cup sugar in a food processor until very finely ground. Mix in the remaining egg, 2 tablespoons butter, the almond extract, pinch of salt and food coloring. Process, scraping the bowl occasionally, until a thick paste forms. Refrigerate until firm, about 30 minutes.
Roll out the dough into a 10-by-11-inch rectangle on a floured surface. Spread the pistachio filling over the dough almost all the way to the edges. Starting with a short side, roll up the dough into a tight spiral. Wrap in plastic wrap and refrigerate, reshaping the log after 1 hour, until firm, at least 3 hours or overnight.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Slice the log into 1/2-inch-thick rounds. Arrange the rounds 1 1/2 inches apart on the prepared pans.
Bake, switching the pans halfway through, until the cookies are firm and light golden around the edges, 20 to 25 minutes. Let cool 5 minutes on the pans, then transfer to racks to cool completely.