Preheat the oven to 350 degrees Fahrenheit and line 2 baking sheets with parchment paper.
In a large bowl, mash the banana until almost no chunks remain.
Using an electric mixer, beat the banana, melted butter, and sugar until combined, light, and fluffy, about 1-2 minutes. Add the egg yolk and beat again, about minute.
In a separate bowl, whisk the flour, baking soda, and salt until combined. Mix the dry ingredients into the wet until just combined, do not overmix.
Use a spatula to fold in the walnuts and white and dark chocolate chips. Divide the mixture into about 12 cookies and bake for 10-12 minutes or until the edges are golden brown and the middle is still slightly soft.
Let cool for about 5 minutes before transferring to a wire rack to finish cooling. Sprinkle with a pinch of flaky salt if using.