In a large mixing bowl, whisk together the flour, baking powder, and salt.
Add the softened butter (or vegetable shortening) and mix with your fingers or a pastry cutter until the mixture resembles coarse crumbs.
Gradually add the warm water, mixing until a soft dough forms.
Turn the dough out onto a lightly floured surface and knead for about 2–3 minutes, or until smooth and elastic.
Cover the dough with a clean kitchen towel and let it rest for 20–30 minutes.
Divide the dough into 2 equal portions. Roll out one portion at a time into a thin rectangle, about 1/8 inch thick.
Cut the dough into 3-inch squares or triangles using a sharp knife or pizza cutter.
Heat about 2 inches of vegetable oil in a deep skillet or Dutch oven over medium-high heat to 375°F–390°F (190°C–199°C). Use a thermometer to monitor the temperature.
Carefully place 2–3 pieces of dough into the hot oil. Fry for 1–2 minutes per side, or until puffed and golden brown. Turn them gently with tongs or a slotted spoon.
Remove the sopaipillas from the oil and drain them on paper towels.
Serve warm, drizzled with honey, sprinkled with powdered sugar, or coated in cinnamon sugar for a sweet version. For a savory option, pair with soups, stews, or chili.