In a large saucepan, bring water and rice to a boil. Reduce heat; cover and simmer for 15-18 minutes or until liquid is absorbed and rice is tender. Stir in sugar and milk. Refrigerate until chilled. In a small bowl, whisk the eggs, baking powder, salt and vanilla; add to rice mixture. Stir in flour.
In an electric skillet or deep-fat fryer, heat oil to 375°. Shape tablespoonfuls of rice mixture into 2-in. oval shapes. Fry ovals, a few at a time, for 1 minute on each side or until golden brown. Drain on paper towels. Sprinkle with confectioners' sugar and drizzle with honey if desired.