Place cake mix, butter, and 1 egg in large mixing bowl. Blend with mixer on low speed for 1 to 2 minutes, or until well combined and thick. Measure out 2/3 cup batter and set aside. Pat the remaining batter into the bottom of an ungreased 13 x 9 inch baking pan and place in the oven.
Bake until the crust is light brown and puffs up, 15 minutes. Remove pan from oven and place on a wire rack to cool for 10 minutes. Leave the oven on.
Place the reserved crust mixture, corn syrup, dark brown sugar, remaining 3 eggs, and vanilla in same large mixing bowl. Blend with mixer on low speed for 1 minute. Stop machine and scrape down sides of bowl. Increase mixer speed to medium and beat until batter is well combined and the crust mixture has blended, 1 minute more, scraping sides down again, if needed. Fold in the pecans until they are well distributed.
Pour the pecan mixture on top of the crust mixture, smoothing it out with a spatula. Return the pan to the oven.
Bake cake until edges are browned but the center is still a little soft, 40-45 minutes. Slice and serve with vanilla ice cream, if desired.