Preheat oven to 350 degrees F (175 degrees C).

Beat cake mix and water together in a bowl until moist; pour into a 10-inch tube pan.

Bake in the preheated oven until top is golden brown, cracked, and looks dry, 38 to 48 minutes. Set aside 8 hours to overnight.

Whisk eggs, milk, brown sugar, cinnamon, vanilla, and salt together in a bowl.

Cut cake into 12 slices. Dip each slice in the egg mixture to coat.

Melt enough of the butter in a large skillet over medium heat to coat the cooking surface. Cook the cake slices in batches the skillet until golden brown, 2 to 3 minutes per side.