In a large bowl, stir together flour, baking powder, salt and shortening. Slowly stir in water and mix until dough is smooth. Cover and let stand for 20 minutes.
Heat oil in a deep frying pan to 375 degrees. Roll out dough on a floured surface until 1/8-1/4 inch thick. Cut into 3 inch squares, then fry in batches until puffy and golden brown on both sides, around 4 minutes per batch. Drain on paper towels and serve warm with honey.
Nutritional info will be skewed based on the need for a lot of oil for frying. If cooked at the proper temperature, assume a retention of about 1 tablespoon of oil per sopapilla.