Make sure the bananas are frozen solid before blitzing. If the ice cream consistency is too soft to scoop, put it back in the freezer for 10 mins.
Heat oven to 180C/fan 160C/gas 4 and line two large baking sheets with baking parchment. Put the peanut butter, sugar, ¼ tsp fine table salt and chocolate chunks in a bowl and mix well with a wooden spoon. Crack in the egg and mix again until the mixture clumps together and forms a dough.
Break off chunks of dough (about the size of a cherry tomato) and arrange them, spaced apart, on the sheets. Press the cookies down with the back of a fork to squash them a little. (The cookies can be frozen for up to two months – to cook from frozen, add an extra 1-2 mins to the cooking time.) Bake for about 12 mins until golden around the edges and paler in the centre. Leave to cool on the trays for 5 mins.
Meanwhile, put the bananas, cream and vanilla in a food processor and blend until they make a thick ice cream. Scoop into balls with an ice cream scoop, and sandwich between the cookies. Serve immediately.