Combine dry ingredients. Combine flour, baking powder, sugar, and salt in a large bowl. Whisk to mix well.
Add coconut oil. Work coconut oil into the dry ingredients with your fingers until it is in small pea-sized pieces.
Add water. Drizzle in warm water while mixing the dough with your other hand. Keep mixing until a soft dough forms. Knead dough until is is smooth and springy, about 4-5 minutes.
Rest. Form dough into a ball and return to the bowl. Cover with plastic wrap and let rest 20 minutes.
Roll out dough. Place dough on a lightly-floured work surface and roll into a rectangle shape until it is about 1/4-inch thick. You can divide the dough in two pieces and roll out in batches if you have limited counter space. Cut into 3x3-inch squares with a sharp knife or a pizza cutter.
Heat oil. Pour oil into a pot deep enough so the oil only comes about halfway up the sides. Attach a deep-fry thermometer to the side. Heat over medium-high heat until it reaches 375°F.
Fry sopapillas. Add sopapillas squares a few at a time. If they have stuck to the counter, run a small spatula or knife underneath the dough to dislodge. Fry until golden on one side, about 1 minute. Flip and let fry on the other side about a minute more. Remove with a bamboo skimmer or a metal slotted spoon to a paper towel-lined baking sheet.
Serve. Dust sopapillas with powdered sugar, cinnamon-sugar, or drizzle with honey (or any combination of the three) and serve immediatley while still hot.