Preheat the oven to 350F. Grease a 10.5x7" baking dish or 8" cast iron skillet with butter. Set aside.

Brown the butter. Add the butter to a saucepan over medium-high heat. Allow to melt and slightly brown, while stirring continuously (~5-8 mins). Remove from heat and set aside to cool slightly (~5-10 minutes).

While the brown butter is cooling, in a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

Once the brown butter is slightly cooled, add the brown sugar and granulated sugar. Whisk to combine.

Then, add the eggs and vanilla, and whisk until smooth and creamy.

Add the dry ingredient mixture to the wet, and fold until just combine.

Fold in the chopped chocolate or chocolate chips until evenly dispersed.

Spread the cookie dough into the prepared baking dish or pan.

Bake at 350F for 25-33 minutes, until the edges are puffy and slightly crispy, while the center is still gooey and slightly underbaked. If you want the center to be more done, you can tent the top of the baking dish with foil, and continue baking for another 5-10 minutes.

While baking, prepare the salted caramel (if using). Mix together the ingredients in a medium bowl, until well combined and smooth. You can adjust the runniness to your liking by adding more maple syrup, if desired!

Remove the deep dish cookie from the oven and top with flaky sea salt.

Serve warm with a scoop of vanilla ice cream and salted caramel, if desired.