Begin by making the dough. To your stand mixer, add the flour, sugar, salt, and yeast. Mix on low until just combined.
Then, add the butter, vegetable oil, warm milk, and egg. Be sure the milk is about 100-110 degrees F. You do not want the milk too hot, otherwise it will kill the yeast and scramble the egg.
Once well combined, scrape down the sides and bottom of the bowl. Continue to mix for 3-5 minutes or until the mixture resembles a soft dough. Be sure to mix for at least 3 whole minutes.
Once fully kneaded, place a towel over the bowl and set it in a warm place for 2 hours. Allow the dough to rise and become bubbly.
After 2 hours, make the filling and preheat the oven to 350 degrees F. Mix all filling ingredients to form a thick, sugary paste.
Dump the dough out onto a parchment-lined baking sheet. With wet fingers to keep from sticking, press the dough out into a rough rectangle shape. Also, grease a loaf pan very well.
Spoon the filling onto the flattened dough. Using a bench scraper and the parchment, roll the dough over onto itself to form a log shape.
Add the sweetened dough log to the greased loaf pan. Bake in a preheated oven for 40-45 minutes or until a cake tester comes out clean and the cake feels hollow when lightly tapped.
Allow the cake to cool for 20 minutes before turning it out onto a cooling rack. Once cooled, serve in big slices.
Warm the slices of cake in the microwave for 10-second bursts, if desired. Store in an airtight container.