Add all applesauce ingredients to a sauce pot set over medium-high heat. Cover and bring to a boil. Stir, reduce heat to medium and simmer 20 minutes, covered, mixing every so often to help cooking.
Grate sweet potatoes and onion using the largest setting on a box grater. Spread potatoes and onions on a paper towel, cover with more paper towels and press to remove as much water as possible, set aside.
Whisk together egg, flour, cinnamon, and salt. Stir in potatoes and onions, mixing to combine. Warm about 1/4-inch of olive oil in a skillet over medium-high heat. Place a scoop of potato mixture into the pan and flatten with a spatula. Fry until darkly golden, about 6 minutes, flip and fry another 5 to 6 minutes. Transfer to plate lined with paper towels and continue. Serve with applesauce.