In a mixing bowl, combine the yeast, warm water, and about a teaspoon of sugar. Let it stand for 5 minutes, or until it becomes foamy.
Add the warm milk, egg, softened butter, sugar, and salt to the bowl. Stir everything together using a wooden spoon.
Gradually add the flour while stirring, just until the dough gathers in the center of the bowl, forming a soft and shaggy mass. You may not need all of the flour.
Transfer the dough onto a lightly floured surface. Knead it until it becomes smooth, elastic, and can stretch thinly. Add flour sparingly as needed to prevent sticking.
Shape the dough into a ball and place it in a bowl. Cover the bowl with a kitchen towel and let the dough rise for 1 to 1 and 1/2 hours, or until it doubles in size.
Gently deflate the dough and divide it into 14 portions. Shape each portion into a smooth ball and arrange them on two greased 9-inch baking pans, spacing them evenly.
Loosely cover the pans with a kitchen towel and let the dough rise once more for about an hour, or until it doubles in size again.
Preheat the oven to 350°F. Beat one egg and brush the surface of the rolls with it.
Bake the "pan de siosa" for 18-22 minutes at 350°F, or until the buns are lightly golden.
Brush the surface of the buns with melted butter, sprinkle them with sugar, and top with shredded cheese.