In a large mixing bowl, combine the all-purpose flour, baking powder, sugar, and salt. Whisk together until well combined.
Add the vegetable shortening to the flour mixture. Use your fingers or a pastry cutter to work the shortening into the flour until it resembles coarse crumbs.
Gradually add the lukewarm water and milk to the flour mixture. Stir until the dough comes together. If it feels too sticky, add a little more flour until you reach a smooth consistency.
Turn the dough out onto a lightly floured surface and knead gently for about 2-3 minutes, until the dough is smooth and elastic.
Using a rolling pin, roll the dough out to about 1/4-inch thickness. Cut into 2-inch squares or triangles using a sharp knife or pizza cutter.
In a deep frying pan or pot, heat about 2 inches of vegetable or canola oil to 375°F (190°C). You can test the oil by dropping in a small piece of dough; if it sizzles and rises to the surface, it’s ready.
Carefully drop a few pieces of dough into the hot oil, making sure not to overcrowd the pan. Fry for 1-2 minutes on each side, or until golden brown and puffy.
Using a slotted spoon, remove the sopapillas from the oil and place them on a plate lined with paper towels to drain excess oil. While they are still warm, toss them in a mixture of sugar and cinnamon.