Melt 10 TBLS butter over medium heat till it becomes browned, stirring. (about 4 minutes) Take off heat, pour into large bowlk and add the other 4 TBLS butter to cool it and add back moisture. Set aside.
In a seperate bowl whisk together flour, baking powder, and baking soda. Set aide.
Mix 1/2 cup dark brown sugar and the regular sugar in a flat dish. Set aside.
Add 1 3/4 cup dark brown sugar into the melted butter till there are no clumps. Add the familla and salt, followed by the egg and then the egg yolk. Mix well. Let sit 3 minutes, then whisk 30 seconds. Do this cycle 3 times to break down the sugars.
Add flour mixture just until well combined.
Roll spoonfuls of cookie dough into balls, roll in sugar mixture and put on baking stone or parchment-lined baking sheet. They'll spread out without flattening the balls.
Bake 12-14 minutes, spin 1/2 way through cooking. They'll look underdone, but when edges well-set, take out! Let them sit on the baking sheet for a few minutes, then cool on baking rack.