Preheat oven to 375°F / 190°C. Grease a large 12-inch cast iron skillet with cooking spray. In a small bowl, combine 250g flour and 1½ tsp Kosher salt, then set aside.
Brown the butter. In a medium saucepan, add 227g butter and melt over medium heat until butter is brown and nutty, about 5-6 minutes, swirling the pan every minute or so.
Cream the butter. Place 330g brown sugar in the bowl of a stand mixer with paddle attachment fitted. Pour browned butter on top, then mix until just combined. Let sit until butter has cooled completely, about 30 minutes. Once cool, beat the butter and brown sugar on medium high speed until light and fluffy, about 2 minutes, scraping down the sides as needed.
Add remaining wet ingredients. Add 2 large eggs, one at a time, beating after each addition, then add 1 Tbsp vanilla. Mix until just incorporated, then scrape down the sides again.
Add dry ingredients. Add the flour to the stand mixer in 3 batches, mixing in each addition for about 5 seconds, and then scraping down the sides. The flour should just barely be mixed in. Pour cookie dough into prepared cast-iron pan, then smooth the top with a spatula.
Melt speculoos. Heat 225g (¾ cup) cookie butter in a microwave safe bowl for about 20-30 seconds, just to loosen it up a bit. Spoon about 150g (½ cup) of the cookie butter over the top of the cookie, then use the back of a knife to swirl it into the dough. Reserve the remaining ¼ cup of cookie butter. If using chocolate chips, sprinkle ½ cup on top of the cookie dough.
Bake the skillet cookie. Bake until cookie is browned around the edges and mostly set in the center, about 22-25 minutes (Cook time will vary based on the size of the skillet, as batter may be thicker if using a smaller skillet). The cookie should not look gooey.
Finish and serve. Drizzle remaining cookie butter (reheat if necessary) over the top, then sprinkle with flaky sea salt. Allow the skillet cookie to cool for 20-30 minutes, then cut into wedges or eat directly out of skillet with spoons!