Mix the flour and dry yeast. In a bowl, mix the milk and water and dissolve the sugar and salt in it. Add the flour-yeast mixture and knead everything into a soft, sticky dough. Add the vegetable oil once you're done kneading. Grease your hands and the bowl with vegetable oil and form the dough into a ball. Transfer the dough to the greased bowl, cover with a dishcloth, and let rise in a warm place for 40 minutes.
Grease your hands again and form the dough into small, even pieces.
Now you can fill the dough balls with one of 3 fillings. For the first filling, put some bacon and shredded mozzarella in the middle of a piece of dough, close the dough around the filling, and form it into a ball.
For the second filling, repeat the process with the halved olives and chopped feta. For the third filling, repeat the process with the shredded cheddar.
Preheat the oven to 350°F and distribute the balls in a greased cast-iron skillet. Fill the gaps between the dough balls with shredded mozzarella. Cover the skillet with a dishcloth and let the dough rise in a warm place for about 30 minutes. Brush the egg wash over the dough balls, put the skillet in the oven, and cook for 30 minutes.
In the meantime, you can get started on the garlic sauce. Add all the ingredients to a bowl and mix with an immersion blender into a homogeneous sauce. Once the bread is done baking, spread the garlic sauce all over the warm buns.