Heat oven to 350 degrees. Butter and flour a baking sheet; set aside.
In a medium bowl, whisk together flour, cocoa powder, baking soda, and salt. In the bowl of an electric mixer, cream butter and sugar until light and fluffy. Add eggs; beat until well combined, scraping down sides of bowl if necessary. Add flour mixture, and stir to form a stiff dough. Stir in pistachios and chocolate chips.
Transfer dough to prepared baking sheet; form into a slightly flattened log, about 12 by 4 inches. Bake until slightly firm, about 25 minutes. Cool about 5 minutes. Reduce oven to 300 degrees.
On a cutting board, using a sharp serrated knife, cut biscotti diagonally into 1-inch-thick slices. Arrange biscotti, cut sides down, on baking sheet, and bake until crisp but still slightly soft in the center, about 8 minutes. Serve with pistachio ice cream.