Preheat the oven to 325°F. Heat a well-seasoned 10.25-inch cast iron skillet over medium-low heat. Add 1/2 cup of the butter, brown sugar, corn syrup, salt, and pecans. Cook, stirring frequently, until the butter has melted and the sugar has dissolved. Remove from the heat and set aside.
Melt the remaining 1/2 cup of butter. Add it to a large bowl with the cake mix, eggs, and water. Beat for about 2 minutes to combine. Pour the mixture evenly over the caramel sauce and pecans in the skillet. Bake for45 to 50 minutes or until the cake is set or a toothpick inserted in the center comes out clean. (If you're unsure about your skillet size, it might be a good idea to place the skillet on a rimmed baking sheet or pizza pan to catch any drips that might run over in the oven.)
Allow the cake to cool for about 10 minutes then place and large plate or platter over the skillet and carefully flip it over to turn the cake out onto the plate. (A dish towel works great to assist in this as the pan may still be hot.) Scoop any pecans and sauce remaining in the skillet over the cake. Serve warm.