Step 1: In a large bowl, whisk together the flour, baking powder, and salt. Make sure they are well combined.
Step 2: Add the cold shortening or lard to the flour mixture. Using your fingertips or a pastry blender, cut the fat into the flour until the mixture resembles coarse crumbs with a few pea-sized pieces remaining.
Step 3: Gradually add the warm water to the flour mixture, mixing with a wooden spoon or your hands until a shaggy dough forms.
Step 4: Turn the dough out onto a lightly floured surface. Knead the dough for 5-7 minutes until it becomes smooth, elastic, and no longer sticky. Avoid over-kneading.
Step 5: Place the dough back into the bowl, cover it with plastic wrap or a clean kitchen towel, and let it rest at room temperature for at least 30 minutes. This relaxation time is crucial for tenderness.
Step 6: While the dough rests, heat the frying oil. Pour 2-3 inches of vegetable oil into a heavy-bottomed pot or Dutch oven. Heat over medium-high heat to 350-375°F (175-190°C). Use a thermometer for accuracy.
Step 7: Divide the rested dough into two equal portions. On a lightly floured surface, roll out one portion of dough to about 1/8-inch thickness. Cut the dough into 3-inch squares or triangles using a sharp knife or pizza cutter. Repeat with the second dough portion.
Step 8: Carefully slide 2-3 sopapilla pieces into the hot oil, being careful not to overcrowd the pot. Overcrowding will lower the oil temperature.
Step 9: Fry for 30-60 seconds per side, or until the sopapillas puff up beautifully and turn a golden brown. Gently push them down with tongs if needed to ensure even browning.
Step 10: Using a slotted spoon or tongs, remove the fried sopapillas from the oil and transfer them to a wire rack set over a baking sheet lined with paper towels to drain excess oil.
Step 11: Continue frying the remaining dough pieces, maintaining the oil temperature between 350-375°F (175-190°C).
Step 12: Serve the sopapillas immediately while warm, drizzled generously with honey, sprinkled with cinnamon sugar, or dusted with powdered sugar for a delightful treat.