Beat peanut butter, brown sugar and granulated sugar on medium speed of electric mixer until blended. Add eggs, 1 at a time, beating well after each addition. Beat in vanilla. Add flour, baking soda and salt on low speed, mixing until blended.
Shape dough into 1½-inch balls. Place 2-inches apart on ungreased cookie sheet. Flatten with a fork or potato masher dipped in granulated sugar to 2¾-inch rounds.
Bake in centre of oven for 15 to 18 minutes, or until set and golden. Cool 5 minutes on baking sheet then transfer to wire rack and cool completely.
Soften ice cream slightly until easy to handle. Stir in banana until well blended. Stir peanut butter to soften, then add to ice cream. Marble peanut butter through ice cream with a metal spatula or knife. Don't overmix - there should still be streaks. Return to freezer until firm, about 1 hour.
Spread the bottom side of 1 cookie with about ½ cup ice cream. Top with another cookie; press down slightly. Roll edge of cookie in chopped peanuts. Wrap individually in plastic wrap or aluminum foil and freeze. Repeat with remaining cookies and ice cream. Freeze until firm, about 3 hours. Store in freezer.
Tip: For an easy filling, opt for store-bought banana nut ice cream.