Add the ½ cup brown sugar and ⅛ cup sugar to the bowl and pour in cooled brown butter. Mix together.
Add the ¾ tsp vanilla, ⅓ tsp baking soda, ¾ cup flour, and ¼ cup wheat flour, and mix together. Mixture should be crumbly but come together when pressed.
Add the egg yolk and mix until combined. Fold in the chocolate chunks and toffee pieces.
Scoop 2 Tbsp of mixture and form into a ball. It will be crumbly, so do your best to press the mixture together into a ball. Set on a baking sheet and press down to flatten the cookie. The edges will be rough since the cookie is crumbly. Repeat with remaining mixture.
Press extra chocolate chunks on top of the cookies as desired. Sprinkle with flaky salt, if using. Bake for 8-10 minutes and allow to cool.