1. Weigh or lightly spoon flours and cornstarch into dry measuring cups; level with a knife. Place flours, cornstarch, sugar, and next 4 ingredients (through salt) in a food processor; process 2 times or until blended. Add butter; process until mixture resembles coarse meal. Add 1/2 teaspoon vanilla and eggs; process until dough forms a ball. Wrap dough in plastic wrap; chill 1 hour.
2. Divide dough in half. Roll each half of dough into 30 (1-inch) balls.
3. Add oil to a Dutch oven to a depth of 2 inches. Heat oil over medium-high heat until a thermometer registers 360°. Add half of dough balls to pan; cook 2 minutes or until golden brown. Remove with a slotted spoon; cool on paper towels. Repeat procedure with remaining dough balls.
4. Add honey to a large saucepan over medium heat; bring to a boil. Boil 2 minutes, stirring constantly. Remove from heat; stir in 1/4 teaspoon vanilla. Add fried dough balls to honey mixture, tossing to coat. Cool 2 minutes.
5. Place on a serving platter. Drizzle with any remaining honey, and sprinkle with powdered sugar.