Firstly, preheat the oven to 180C/160C Fan/Gas Mark 4. Then grease a 9x9inch square baking tin, and line the base and two opposite sides with baking paper.
For the browned butter: Place the butter into a small saucepan over a low-medium heat and melt stirring every now and then. Keep the melted butter on the heat as it foams, stirring every now and then until the foaming subsides and you're left with a light brown butter with darker flecks. Then take off the heat and set aside.
For the dough: Firstly, chop the chocolate into rough chunks and set aside. Then add the browned melted butter into a large bowl with both the sugars. Using an electric hand-whisk, whisk on a high speed until well combined. Then add the egg, egg yolk and vanilla and whisk again until well combined. Then whisk in the flour, baking powder, bicarbonate of soda and table salt until you have a soft thick dough. Finally, mix in the chopped chocolate.
Tip the cookie dough into the prepared baking tin, and using your hands flatten in the tin till even. Then bake for 20 minutes until lightly golden brown, then remove from the oven and leave in the tin for 15 minutes. Finally, remove from the tin and leave to cool completely on a cooling rack, sprinkling with sea salt flakes if desired. Then slice into 8 bars.