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1
Combine flour, baking powder, and salt in a wide bowl. Add the shortening or lard and rub between the fingertips until the mixture resembles coarse crumbs with no visible fat pieces remaining. The texture is dry and crumbly throughout.
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2
Add warm water gradually, mixing until a cohesive dough forms. Knead briefly — no more than 1–2 minutes — until the dough just comes together. Excessive kneading develops gluten that will resist puffing. The dough is smooth but not elastic; it yields when pressed.
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3
Cover the dough and rest at room temperature for 30 minutes. The gluten relaxes further; the dough will feel noticeably softer and more yielding than immediately after kneading.
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4
On a lightly floured surface, roll the dough to 3–4 mm thickness. Cut into squares or triangles of roughly 8–10 cm. The sheets should be thin enough to puff readily but thick enough to hold their structure once hollow.
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5
Heat oil in a deep, heavy vessel to 185–190°C. At this temperature a small piece of dough dropped in will sizzle immediately and vigorously. If the oil is cooler, the dough will absorb it before generating enough steam to puff.
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6
This is where the dish lives or dies. Lower one dough piece into the hot oil and immediately press it gently beneath the surface with a slotted spoon or spatula for 3–4 seconds. This brief, even resistance against the hot oil ensures that the steam generated inside the dough puffs the bread evenly from within rather than from one side only. Within 5–10 seconds of contact the sopaipilla will begin to swell and puff hollow.
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7
Fry for 30–45 seconds on the first side, then turn and fry for a further 30–45 seconds. The sopaipilla is done when both sides are evenly golden and the bread holds its puffed, hollow form. Lift and drain on a rack or absorbent paper. Fry remaining pieces in batches, maintaining oil temperature between each batch.