Place 10 tablespoons of the butter in a large microwave-safe bowl and cover with a lid, a plate or another bowl to prevent spattering. Microwave the butter on high power for 4 minutes. Check for color. You’re looking for a deep amber color with some chestnut-colored flakes of brown throughout. Continue cooking for 30 seconds at a time until a deep amber color is achieved. This can take anywhere from 4-7 minutes, depending on your microwave.
Add brown sugar and salt to bowl with cooled butter; whisk together until no sugar lumps remain. Add egg, yolk, and vanilla and whisk together until fully incorporated.
Sprinkle flour, then baking soda and baking powder evenly over the top of the sugar/butter mixture. Mix with a sturdy spatula or wooden spoon until all dry ingredients are incorporated.
Bake one sheet at a time for 10 minutes, then remove from oven and sprinkle with a pinch of flaky sea salt. Return to oven and continue baking until cookies are browned and still puffy and edges have begun to set, but centers are still soft (cookies will look raw between cracks and seem underdone), about 2-4 more minutes. Rotating baking sheet halfway through baking if cookies seem to be baking unevenly. Do not overbake.
See Café Tips above for more detailed instruction and extra tips.