Add 2 inches of olive oil to a medium saucepan. Bring to medium heat (about 335-350°F). Be careful to not let the oil get too hot beyond that because olive oil has a lower smoke point.

While your oil is heating, make the donut dough. In a medium mixing bowl, add flour and baking powder. Whisk until evenly mixed. Stir in the applesauce. Mix with a spatula until a dough forms and applesauce is fully incorporated into the flour mixture.

Once the oil is ready, scoop dough using a 2 tsp cookie scoop. Use a spatula to level and smooth the surface of the scoop. Gently release the dough ball directly into the hot oil. Repeat this with the remaining dough. The donuts will float to the surface so only add in as many donuts as can fit comfortably at the surface of your saucepan. I fried my donuts in two batches since my saucepan can only fit about 5. If a donut sinks and gets stuck to the bottom of the pan, make sure to loosen it from the bottom immediately using your frying spatula strainer. Cook donuts until both sides are golden brown, flipping them halfway through. Remove donuts from oil and place onto a plate lined with a paper towel to soak up excess oil.

 When donuts are no longer too hot to touch, you can coat with cinnamon sugar. You can also leave them plain.