In a bowl, dissolve the yeast in warm milk and a tablespoon of sugar. Let it sit for about 5-10 minutes until it becomes frothy.
In a mixer or mixing bowl, combine the flour, sugar, salt, ½ cup softened butter, eggs, and yeast mixture.
Mix the ingredients until a dough forms.
Knead the dough with your hand on a floured surface for about 10-15 minutes until it becomes smooth and elastic. You can use a paddle attachment or a dough hook if you are using an electric mixer.
Place the ball of dough into a greased bowl and cover with a plastic wrap or damp cloth. Let stand at room temperature until the size is doubled, about 2 hours. It is faster in a relatively warm environment.
Grease your brioche molder with cooking oil or butter. If you don't have a molder, you can use a pie pan, be sure to grease it so the dough won't stick.
Punch down the dough and divide it into 22 equal portions, shaping each portion into a ball.
Roll each ball into a rope, then coil it into a round shape to form the ensaymada. Transfer the rolls to the greased brioche molder. Let the shaped dough rise again for about 1 hour or until the size has doubled.
Preheat your oven to 350°F or 175°C.
Bake the bread in the preheated oven for about 15-20 minutes or until the tops are lightly brown (not golden brown). Time may vary depending on the size of your dough.
While waiting for the dough in the oven, prepare the topping by combining the softened butter and sugar until well mixed.
Once baked, remove the bread from the oven and let it cool. Spread the butter-sugar mixture on the top. Sprinkle the grated cheese. Serve and enjoy your delicious ensaymada!