In a large mixing bowl, sprinkle yeast over the warm milk. Let this stand for about 5 minutes, or until the mixture is foamy. Add the eggs, sugar, oil and the salt to the bowl. Stir everything together using a wooden spoon.
Add 4 cups of flour, one cup at a time. Stir well after each addition until the mixture is starting to come together. Add just enough of the remaining 1/4 cup of flour and keep stirring until the dough gathers into a soft, shaggy mass in the center of the bowl.
Turn the dough over on a lightly floured board. Knead it until the dough is smooth and elastic, adding a little bit of flour to help when the dough is sticking too much. Shape the dough into a ball. Place it in a bowl and cover it with a kitchen towel. Let it rise for 1 to 1 and 1/2 hours or until doubled in size.
Meanwhile, make the filling: Stir together cornstarch and 1 cup of milk in a medium saucepan until the mixture is smooth. Add condensed milk and stir. Cook the mixture over medium heat while stirring constantly. The mixture will start to bubble and thicken. Cook it for 3-4 minutes more, still stirring, until the mixture is thick and falls back in dollops when you lift a spoon. Stir in vanilla extract. Set aside filling while you finish the dough.
Gently deflate the risen dough. Divide it into 14 equal portions. Flatten each dough portion into an oval that is around the same size as your hands. Spoon about a tablespoon of the filling into the upper third section of the oval.
Fold the upper part of the dough over to the center to cover the filling. Seal the edges. Now, use a knife to make slits or strips to the remaining lower portion of the oval. Fold each cut strip over to the center to cover the filling bump yo have made. Repeat with the rest of the dough portions.
Arrange the assembled dough on a large baking pan that is lined with parchment paper. Cover loosely with a towel and let rise once more for about an hour, or until puffy and doubled in size.
Preheat oven to 350 F. Using a pastry brush, brush milk on the buns. Bake at 350 F for 18-22 minutes, or until the buns are lightly golden.