Sopaipilla (pronounced "soap-pa-peeya") is basically a fried pastry. A really good family friend on my man's side of the family is Mexican, and she taught me how to make Tex-Mex style dinners including our favorite - Sopaipilla's. If you've ever been to a carnival, they are basically elephant ears. You can sweetin' them with honey, cinnamon and sugar, powdered sugar, or eat them plain.
We have a deep fryer and I usually set mine to 375 degrees. I've never made these on the stove top, but my Mother-in-law just heats oil in a nice size sauce pan and makes them that way.
Combine self-rising flour and water together into a bowl until you have what resembles pizza dough or bread dough. If it's too dry, add a little bit more water, if too wet, add a little bit more flour. Cover with flour to prevent it from sticking to your hands.
Place dough on a floured surface and roll out until it's about 1/2" thick, or about the thickness of pizza dough.
They don't have to be perfect, just use a butter knife (or even a pizza cutter) and slice them up into squares. I usually get about 13-14 squares each time I make them, depending on how big you cut them.
When the oil is ready, place about 3 or 4 of them in the fryer. They sink down to the bottom then float up to the top. Let cook for 3-4 minutes on one side (or until a nice golden brown), then using a slotted spoon, and being extremely careful, flip them over and let them cook for 3-4 minutes on the other side.
When they are complete, remove them with a spoon and place them on a plate covered with paper towels to let the oil drain off as well as let them cool. I have a cinnamon/sugar mixture that we keep in a salt shaker and I cover them with that as soon as they come out of the fryer. As the oil drains off, it sorda acts like a glue for the cinnamon and sugar.