1. Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius).
2. Wash and dry apples. Cut off the top quarter of each apple. (You can reserve the tops to add to the pan as extra baked apple bits, or just eat them.) Core the centers of the apples, taking care not to cut through to the bottom of the fruit; discard cores.
3. Cut two circles around the hole in the center of each apple, one wider than the other, again taking care not to cut all the way through. Then cut slices, going around each apple, but again not cutting through to the bottom of the fruit. (You can use an apple cutter if you have one, cutting almost to the bottom, and forming segments/sections of the apple all around.) You now have an apple flower shape.
4. Place apples into a baking pan, leaving space between each one to allow for spreading of “petals.”
5. In a small mixing bowl, stir together oil, sugar, cinnamon, and water until well combined. Pour sauce over the apple flowers, working to get the liquid to run down the cuts in the fruit. Sprinkle with potato starch and cover the pan with foil.
6. Bake for 50 minutes and check for doneness. The apples should be soft and spread out a bit yet still holding their shape. Baste with sauce and return to the oven for five more minutes, uncovered.
7. Serve warm, with a scoop of vanilla ice cream in the center hole and drizzled with accumulated cinnamon syrup.