Grease a 9"x13" baking dish or line with parchment paper. Set aside.
to make the cake base:
In a measuring cup, combine milk, warm water and a dash of sugar. Sprinkle yeast over the surface and give it a few stirs. Let sit until foamy, about 5 minutes.
Preheat oven to 220 degrees F. (this step is optional; it just cuts down on a rising time)
In the meantime, cream butter, sugar and salt in a large mixing bowl of your stand mixer. Beat on medium speed until light and fluffy, about 2 minutes.
Add egg and mix well.
Add flour alternating with yeast mixture until smooth dough forms. The dough will be sticky but should not be wet. It will not pull away from the sides of the bowl.
Transfer the dough onto prepared baking dish and patting with your hands, spread it to cover entire bottom of the dish. It may take a while so be patient.
Cover the dish with a kitchen towel and set in a warm and draft-free place to rise for 2 to 3 hours OR preheated but turned-off oven for about 30 minutes.
Once the base is ready, take it out of the oven and preheat the oven to 350 degrees F.
make the filling:
In a small measuring cup or a bowl, mix together corn syrup, water and vanilla extract. Set aside.
In a large mixing bowl of a stand mixer, beat butter for 20 seconds. Gradually add sugar and cream together until light and fluffy. Scrape down the sides of the bowl as needed.
Mix in the egg.
Add the flour alternating with corn syrup mixture. Beat together until smooth.
Drop dollops of the filling over the cake base. Spread with a spatula and smooth out the top.
Bake for 25 to 30 minutes or until the top is golden brown. The topping will be gooey.