In a bowl, cream together 1 1/3 cup butter and 1 1 /3 sugar. Set aside and reserve for filling and topping ensaimada rolls.
Place divided dough on a lightly floured work surface. Lightly cover the dough with plastic wrap or a kitchen towel to prevent dough from drying out.
Working with one portion at a time, use a small rolling pin to flatten and stretch dough into a 6-inch square. Lightly flour work surface as necessary.
Spread about 1/2 tablespoon of creamed sugar butter over surface of dough. Sprinkle a little grated cheese on top.
Starting with the edge of the dough closest to you, roll dough into a log. Using both palms, gently roll and stretch log to about 10 inches long. Roll right hand upward while you roll left hand downward to twist the log of dough.
Shape twisted log into a snail-like coil. Pinch the end of the coil into the bottom of the roll. If using jumbo muffin tin, place coil in lightly buttered mold. Otherwise, place coil on a parchment lined baking sheet.
Continue and repeat with remaining portions of dough. Once all the dough has been shaped, cover dough with plastic wrap and let sit for 45 minutes until dough has risen.
Preheat oven to 325 degrees F. Bake ensaimada rolls for 20-25 minutes. Rotate pans halfway through baking. When rotating pans, spread a little bit of creamed butter mixture over rolls. Bake until the tops of the bread are lightly golden brown or until the internal temperature of dough is at least 185 degrees F. Let cool in pan for a couple minutes. Then transfer to a wire rack.
Once rolls have cooled to room temperature, take remaining creamed sugar butter mixture and grated Edam cheese. Spread creamed butter over the tops of the bread, sprinkle cheese over butter.
Before serving, warm up ensaimadas in the microwave for about 20 seconds to melt the cheese and fluff up the bread. *When reheating bread in the microwave, keep a mug of water in the microwave to keep bread moist and prevent bread from becoming gummy.