Sift the dry ingredients together in a large mixing bowl. Add the shortening and water, work them in with your hands to make a soft, pliable dough. Add more water, 1 teaspoon at a time, if the dough feels too dry. Gather the dough into a ball and wrap in plastic wrap. Put the dough in the refrigerator and chill for at least 1 hour so it will firm up a bit and be easier to roll and cut. (Dough can be prepared 1 day ahead, refrigerated.)
Unwrap the ball of dough and put on a lightly floured surface, cut in half. With a floured rolling pin, roll each piece of dough into a circle, about 1/4-inch thickness. Using a paring knife or pizza cutter, cut the dough into triangles as you would a pizza. You should end up with 6 or 8 triangles per circle.
Heat 2-inches of oil to 375 degrees F in a heavy skillet or deep pot over medium-high heat.
Fry a few of the sopapillas at a time, keeping an eye on maintaining the oil temperature. As the sopapillas puff up and rise to the surface, flip them over with a slotted spoon, skimmer, or chopsticks; about 2 minutes on each side. Carefully remove the sopapillas from the oil and drain on several layers of paper towels or a brown paper bag. Cool slightly. Serve hot with honey or cinnamon sugar.