Preheat the oven to 350 degrees F.
In a bowl, whisk together the flour, baking powder, soda, and salt.
Heat an oven safe (preferably cast iron!) 12-inch skillet over low heat. Let the skillet heat up for 5 minutes. Add the butter and let it melt completely. Stir in the sugars with a wooden spoon. Turn off the heat under the skillet. You MUST turn off the heat! You can also remove the skillet from the burner if you wish.
Whisk together the egg and egg yolks in a bowl. Add it to the skillet sugar mixture and mix in right away with a spoon, quickly mixing so the eggs don’t cook from the heat. Stir in the vanilla extract.
Stir in the dry ingredients until just combined. This will take a minute or two and the mixture will be thick, but they will mix in! You can wipe the top of the skillet or the sides with a damp paper towel to remove excess flour.
Stir in the chocolate chips. Bake the skillet cook for 20 to 25 minutes, or until it’s mostly set in the center. Top with flaked sea salt.
Serve warm with vanilla ice cream.