Prepare 2 baking sheets. You can grease them or use parchment paper.
In a medium bowl, mix with a spoon 1-½ cups milk, 2 tablespoons sugar, 2 teaspoons dry yeast and 1 cup flour. Cover with a kitchen towel and let rest 40 minutes.
In a large bowl add 3-¼ cups flour, 1 teaspoon salt, and 1 egg. Add the yeast mixture and mix.
Place the dough on a flat surface and knead for 5 minutes; add the butter and continue kneading until the dough is smooth. If the dough is very sticky, flour your hands to knead.
Grease a large bowl with vegetable oil. Place the dough in the bowl, turn the dough over so that it is coated with oil. Cover the bowl with a kitchen towel and let it rest in a warm place. Let stand until double its size. This can be anywhere from 1 hour to 2, depending on the weather or the temperature in your house.
Cheese topping: In a small bowl, beat 1 egg. Use only half for this topping. Add milk and cheese; Mix.
Sweet topping: In a medium bowl, beat the butter or the desired fat you want to use, until creamy. Add the sugar and flour; mix well.
Place the dough back on a flat surface and divide into 16 equal portions. If you want them all to be the same size, weigh your dough and divide it by 16. Then weigh each portion.
Shape each ball by pressing it between the palm of your hand and the table in a circular motion until they’re round.
Flatten them with the palm of your hand and place them on the prepared trays.
Preheat the oven to 350F/180C.
When the oven is hot. Flatten each piece of roll again with the palm of your hand or with your fingers. Add the cheese topping to 8 of the rolls, and the sweet topping to the other 8 rolls.
Bake for 25 to 30 minutes, or until golden brown.
Remove from the oven and place them on a cooling rack.