Bring stock to a boil. Lower heat to just keep hot. Line a baking sheet with sides, with wax paper.
Peel onions and cut into fine dice. Heat olive oil, add onions and saute for 5 minutes, until slightly browned. Add the rice and stir to coat with oil. Add 2 cups of stock and bring to a simmer.
Simmer for 20 minutes, adding stock, 1/2 cup at a time, every 3 minutes, until you have used all the stock. Stir in parsley and butter. Taste and adjust seasoning with salt and pepper.
Pour out into lined pan and smooth top. Set aside to cool. Place cornmeal on a plate, set aside. When rice is cool, divide it into either six or twelve equal portions.
Press each portion into a 3-inch ring mold or pastry cutter to form a firm cake. Place cakes in cornmeal to coat each side generously.
Heat vegetable oil in a large saute pan over medium heat. Add the cakes and cook for about 2 minutes per side. until crisp and golden.