Combine the butter and sugar in a large bowl. Using a hand mixer, beat the mixture until light and creamy, about 2 minutes. Add the cocoa powder, vanilla, salt and egg and beat again until smooth and combined. Add the flour, peanut butter chips and chocolate chips. Use a rubber spatula to stir until just mixed.
Line 2 baking sheets with parchment paper. Scoop out 2-inch balls of dough. Place 14 on each baking sheet. Bake, rotating halfway through, until the cookies are just set around the edges and the tops look dry, about 15 minutes. Let cool for 15 minutes on the baking sheets. Remove to a wire rack to cool completely.
When the cookies are completely cool, scoop a heaping tablespoon of the ice cream onto the flat side of one cookie. Top with another cookie and press together gently. Continue with the remaining cookies and ice cream, freezing the sandwiches as you go.