For The Cake, Place The Milk In A Small Saucepan Over Medium Heat For About 1 Minute, Or In The Microwave On Low Power For 45 Seconds, And Heat Until The Milk Is 100°F.
Sprinkle The Yeast Over The Milk, And Stir To Dissolve.
Set Aside.
Place The Butter, Sugar, And Salt In A Large Bowl, And Beat With An Electric Mixer On Medium Speed Until Light And Fluffy, 2 To 3 Minutes.
Add The Egg, And Beat Until Incorporated.
Stop The Mixer, And Scrape Down The Sides Of The Bowl.
Add The Flour Alternately With The Yeast And Milk Mixture, Beginning And Ending With The Flour.
When All The Flour Has Been Added, Blend On Low Speed Until The Dough Is Smooth And Elastic, About 5 Minutes.
Lightly Rub Butter Into The Bottom Of Two 8″ Square Pans.
Divide The Dough In Half, And Press One Half Into The Bottom Of Each Pan.
Cover Each Pan Loosely With Plastic Wrap, And Place In A Warm Place To Rise Until Nearly Doubled, About 2 Hours.
When The Dough Has Nearly Finished Rising, Make The Filling.
Place The Butter, Sugar, Salt, And Corn Syrup In A Large Mixing Bowl, And Beat On Medium Speed Until Light And Fluffy, About 3 Minutes.
Scrape Down The Bowl And Add The Vanilla And 1 Egg.
Beat On Medium Speed Until Combined, Then Add The Second Egg.
Add The Milk And Half The Flour, Beating Until Combined.
Add The Rest Of The Flour, And Beat Until Smooth.
Set Aside.
Place A Rack In The Center Of The Oven, And Preheat The Oven To 350°F.
Pour The Filling Over The Rising Dough, Dividing It Evenly Between The 2 Pans, And Spread It To The Edges.
Place The Pans In The Oven.
Bake The Cakes Until The Tops Are Golden Brown, 25 To 30 Minutes.
Remove From The Oven, And Let The Cakes Cool For 20 Minutes.
Dust With Confectioners’ Sugar, Slice, And Serve Warm.
