Pre-heat oven to 175°Celsius.
Place both the brown sugar and granulated sugar in a bowl.
Add peanut butter and butter and beat until the mixture turns creamy.
Peel and mash the banana and add it to the creamed mixture. Beat until well incorporated.
Sift the flour, baking soda and salt. Add it to the banana mixture. Mix until well combined.
Reserve about ¼ of the milk and white chocolate chips. Add the remaining to the cookie dough and mix with a spatula. At this stage, the dough will be sticky.
Cover the mixing bowl and chill the dough for approximately 30 minutes.
Remove dough from oven and scoop the cookie dough into one tablespoon size. Drop them onto a parchment-lined baking tray, making sure they are well spaced. Shape them lightly into round balls.
Press the remaining chocolate chips onto the cookies.
Bake the cookies for approximately 7 minutes at 175°Celsius until the sides are slightly brown.
Remove the cookies from the oven and press in more chocolate chips if you wish. The cookies will be soft as soon as they are out of the oven.
Cool the cookies completely before serving.