Chocolate Peanut Butter Cookie Sandwiches

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1 cup (2 sticks) unsalted butter, at room temperature

1 cup sugar 

1/2 cup unsweetened cocoa powder 

1 teaspoon vanilla extract 

1/2 teaspoon kosher salt 

1 large egg, at room temperature 

1 1/2 cups all-purpose flour 

1/2 cup peanut butter chips

1/2 cup mixed chocolate chips, such semisweet, bittersweet or white chocolate chips 

1 pint chocolate-peanut butter ice cream, softened slightly