In a large mixing bowl, combine the flour, baking powder, and salt. Mix well.
Add the vegetable shortening or lard to the flour mixture and use your fingers or a pastry cutter to blend until the mixture resembles coarse crumbs.
Gradually add the warm water, mixing until a soft dough forms. Knead the dough on a lightly floured surface for about 2-3 minutes until smooth.
Cover the dough with a clean kitchen towel and let it rest for 30 minutes.
After resting, roll out the dough to about 1/4 inch thick. Cut into squares or triangles, about 2-3 inches in size.
In a deep skillet or pot, heat oil over medium-high heat (about 350°F).
Carefully drop the cut dough pieces into the hot oil, frying until they puff up and turn golden brown, about 1-2 minutes per side.
Remove the sopaipillas with a slotted spoon and drain on paper towels.
Serve warm with honey drizzled on top or dusted with powdered sugar.