According to Wikipedia, a legend about the cake's origin is included in Saint Louis Days...Saint Louis Nights, a cookbook published in the mid-1990s by the Junior League of St. Louis:

The cake was supposedly first made by accident in the 1930s by a St. Louis-area German American baker who was trying to make regular cake batter but reversed the proportions of sugar and flour.

But then again, according to What's Cooking America, at least two families take credit for the cake. The first is the Danzer family:

 

In late 1942 or early 1943, Johnny Hoffman of St. Louis Pastries Bakery was working on a Saturday and made what eventually turned out to be Gooey Butter Cake. You're right, it was a mistake! He subsequently called Herman Danzer, my dad, and told him he thought he may have something and asked to come to my dad's shop on Spring & Gravois to see if they could duplicate it.

They worked all Saturday, and through many trials and errors got it pretty good. The final batch they made, my dad suggested they add glycerin to get it really gooey. It worked - whereupon my mom, Melba Danzer, came into the shop from the store to see what these two guys were doing. When she tried it she said "this sure is gooey" subsequently, the name.

And then there's the Koppe family:

 

My father, John Koppe, a St. Louis baker, also developed the Gooey Butter Cake in the early 1940s...he owned and operated Koppe Bakery during World War II on California and Arsenal Streets in South St. Louis. His shop was located on the corner of two major bus lines, so people who were transferring would often stop in while waiting for their bus.

The Gooey Butter Cake was a smash hit with customers. The lines of customers spilled out the door and around the block. This cake was very gooey, rich, and exceptionally delicious! I remember that the goody butter cake is best described as very "GOOEY." You could eat it with a spoon! The top was sprinkled with powdered sugar and the edge was slightly crispy to hold it together - almost like a pudding. It was baked in a square shape and, of course, was light colored, like butter.

But while the cake's origins may be up in the air, one thing's for sure: it's a St. Louis institution. One company, Gooey Louie, specializes in a variety of takes on the Gooey Butter cake, including a variety of different flavors (including a "design-your-own-flavor" feature) as well as individual-serving cakes and tiny "Gooey Butter Bites". Around the St. Louis area it's a common cake to find in bakeries. Though not as common elsewhere, at least one savvy Cake Gumshoe sighted a version of it in a Seattle area Safeway!

And happily, another Cake Gumshoe, Kerry of Lollicakes, was brave enough to try out the recipe to see for herself. Here's the recipe she used:

 

The Best St. Louis Gooey Butter Cake Recipe

Ingredients:

• 1 box yellow cake mix with pudding in the mix (Pillsbury works best) 
• 4 extra large eggs 
• 1 stick melted butter 
• Pure vanilla extract 
• 1 8 oz. package cream cheese 
• 1 box powdered sugar (3 1/2 cups)
• Crisco or pam for greasing pan

Equipment:

• 9 X 13 Pan 
• Mixer 

Directions:

 

BUTTER CAKE MIXTURE:

1. Get 9 x13 pan and grease with Crisco on the bottom and all sides. 
2. Put yellow cake mix in mixing bowl. DO NOT FOLLOW THE DIRECTIONS ON THE CAKE BOX. Add 2 extra large eggs, 1 stick of melted butter in microwave about 35 seconds, and 1/2 tsp. pure vanilla extract. Mix together in mixer. Batter will have a very most feel to it. Take cake batter and spread evenly through 9 x 13 pan so it evenly covers the bottom of the pan. 
3. Clean off mixers and mixing bowl. 

GOOEY MIXTURE:

 

 

1. Melt cream cheese in microwave about 45-50 seconds. 
2. Put 3/4 of the powdered sugar in mixing bowl setting aside about 1/4 of the box for topping to sprinkle on after the cake is baked and cooled. In mixer add 3/4 powdered sugar, melted cream cheese, and 2 extra large eggs. Mix together in mixer. This will have a very GOOEY consistency as this is the gooey part of the cake. Take the Gooey mixture and layer on top of the cake batter mixture in pan. 

COOKING INSTRUCTIONS:

1. Here at sea level we bake it at 350 for 30-40 minutes or until the top of the cake is browned (Note: Kerry baked hers for 35 minutes and thought it was perhaps slightly over-baked). You want to make sure the gooey mixture on top of the cake is not too gooey otherwise it will be like a liquid. It is okay if the edges are brown and the top of the cake is lightly browned as well. 
2. Once cooked remove from oven and let cool about two hours before cutting and adding remaining powdered sugar. Add remaining powdered sugar to coat/cover top of cake, cut like brownies and serve. 

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