Place rice flour into a shallow dish. Whisk egg whites and egg together in another shallow dish. Mix bread crumbs with oregano, salt, pepper, garlic powder, onion powder, and turmeric in a third dish.
Dredge one mozzarella stick through the rice flour, making sure to cover all four sides and the ends. Tap off excess flour, then dip stick into the egg mixture; turn with a fork to coat completely. Drain off any excess egg. Dredge thoroughly through the rice flour and eggs again. Shake off excess, then roll into the bread crumb mixture. Dip once more into the eggs and coat with bread crumbs again, covering the ends to prevent the cheese from melting and leaking through. Place stick on a freezer-safe plate. Repeat process for each mozzarella stick.
Cover the plate of mozzarella sticks with plastic wrap and freeze for 30 minutes. Preheat the oven to 425 degrees F (220 degrees C). Line a baking sheet with parchment paper. Set the timer for another thirty minutes.
Fill an oil sprayer with olive oil. Remove sticks from freezer and arrange on the prepared baking sheet; spray tops with olive oil.
Bake in the preheated oven for 5 minutes. Remove from oven and close oven door; turn sticks over and spray with oil. Continue baking for 5 minutes more. Continue turning, spraying, and baking the remaining two sides, about 10 minutes more.