After 30 minutes, cut the dough in 4, and roll each piece into a small, smooth ball. You can also skip cutting the ball into pieces, and just roll the entire piece, its just harder to work with it this way.
One by one, roll out each ball on a floured surface into an imperfect rectangle that is about 1/8-1/4 inch thick. Cut into 3 inch squares and arrange them on a tray that has been covered with parchment paper.
Add oil to a deep pan, saucepan or deep-fryer. If using a pan/saucepan, you need to fill it with at least 4 inches of oil.
Once the oil is hot, 375 degrees F, add Sopapillas a few at a time and fry until golden brown on both sides.
It is important to not add too many at the same time, depends how large is the pan or pot you are using. They should have enough room to puff up. Also, it is very important to move them around. Use chopsticks or two forks, to move them around the pan and turn on the other side.
Sopapillas have airy centers, they should inflate almost like balloons when added to the hot oil. When moving them around, turning or removing them from the pot, be gentle and careful, to not pierce them.
Cook only until golden brown on each side. Remove and place on a cooling rack that has been placed inside a baking dish. This is done to drain any remaining excess oil.