In a large mixing bowl, gently whisk together the all-purpose flour, baking powder, and salt.
Add the shortening to the dry ingredients. Use a pastry blender or a fork to cut it in until the mixture is crumbly and well combined.
Slowly stir in the warm water until a soft dough begins to form.
Knead the dough right in the bowl for about 2 to 3 minutes until it feels smooth and pliable. Be careful not to overwork it.
Place the dough in a clean bowl, cover it tightly with plastic wrap, and let it rest for 15 minutes. This makes it easier to roll.
While the dough rests, pour the vegetable oil into a heavy-bottomed skillet or Dutch oven, ensuring it's about 2 inches deep. Heat the oil to a temperature of 350°F to 360°F.
Turn the rested dough out onto a lightly floured surface. Roll it into a rectangular shape, approximately 9 by 12 inches.
Using a pizza cutter or a sharp knife, cut the dough into 12 equal squares or rectangles. Feel free to adjust the size if you prefer smaller or larger sopapillas.
Carefully place the dough pieces into the hot oil in batches, making sure not to overcrowd your pan. Fry each sopapilla for 1 to 2 minutes per side, until they puff up beautifully and turn a lovely golden brown.
Using a slotted spoon or spider, remove the fried sopapillas and place them on a plate lined with paper towels to drain any excess oil.
If you like, sprinkle with powdered sugar and drizzle with honey while they are still warm. Serve immediately and enjoy!