Place salted butter in a pan and let it simmer with continuous stirring until the milk component of butter turned brown and you can smell a nutty odor from the toasted butter. Immediately add the cold water and keep stirring. Set a side to cool to room temperature.
Sift together all purpose flour, matcha green tea powder, baking powder and baking soda. Set a side.
Cream together the cooled roasted butter, brown sugar, white sugar, vanilla extract, egg and egg yolk. Beat using a hand mixer for 2 to 3 minutes at medium speed.
Add a third of the flour mixture into the sugar mixture and mix with the hand mixer. Add another third and mix. Do the same with the last third of the flour mixture. Mix until the flour is just incorporated into the sugar mixture.
Add the chocolate chips and mix using a wooden spatula. Cover with a cling wrap and refrigerate for 12 to 48 hours before baking.
Preheat the convection oven to 180 degrees Celsius.
Using a half ounce ice cream scooper, scoop the batter onto the baking sheet lined with baking paper. Add two to three pieces of chocolate chips (Optional). Sprinkle with a little salt. Bake for 7 to 8 minutes.
Remove the baking sheet from the oven and let the cookies cool on the baking sheet for three minutes before transfering onto a cooling rack.