Preheat oven to 350 degrees F and line baking sheets with parchment paper. In a medium mixing bowl, sift together flour, baking soda and salt and set aside. In a stand mixer with the paddle attachment, cream the butter, peanut butter, sugar and brown sugar until light and fluffy – about 8 minutes. Add egg and vanilla extract and beat until thoroughly combined. Reduce mixer to low, slowly add the flour mixture and beat until just combined.
Using a small ice cream scoop (1 3/4 inch), scoop dough into 1-1/2 inch balls and roll in remaining 1/4 cup sugar to coat evenly and place on baking sheet about 2-inches apart. Gently press the cookies with the back of a fork to create a crisscross pattern (if tines stick, dip fork in cup of warm water in between each cookie). Transfer baking sheets to oven and bake 12–15 minutes, or until just golden. Transfer to cooking racks and let cool completely before making sandwiches.
Slice bananas into 1/8-inch thick slices and fan slices on bottom sides of 12 cookies. Place 1 small scoop of chocolate chip ice cream on top of the banana slices and top with remaining cookie. Serve immediately or wrap cookies individually in plastic and freeze.