Place the rice, flours, baking powder, sugar, cinnamon, nutmeg and pecans into a mixing bowl. Mix well. Stir in the beaten eggs and vanilla. Set aside.
Heat the oil in a large saucepan over medium-low heat. Using a pair of oval tablespoons, shape the dough by taking a heaped tablespoon of it and using the other spoon to form and quenelle. The dough will be sticky and firm enough to do this.
Drop the shaped batter into the hot oil and fry for several minutes, or until golden. You can cook a few at a time. When cooked, drain on kitchen paper as you cook the rest of the dough.