Follow these detailed steps to ensure your patties are perfectly formed, gloriously golden, and irresistibly crispy every time. The key is a gentle touch when mixing and a hot pan for frying.

1. Prepare the Rice Base: In a large mixing bowl, place your 3 cups of chilled, cooked rice. If the rice is in large clumps from being in the refrigerator, use a fork or your hands to gently break it apart until the grains are mostly separated.
2. Combine the Wet and Dry Ingredients: To the bowl with the rice, add the 2 large eggs, 1/2 cup of grated Parmesan cheese, 1/2 cup of shredded cheddar or mozzarella, 1/4 cup of all-purpose flour, 2 tablespoons of chopped chives, 1 teaspoon of garlic powder, 1/2 teaspoon of salt, and 1/4 teaspoon of black pepper.
3. Mix Gently but Thoroughly: Using a spatula or your hands, mix all the ingredients together until they are just combined. Be careful not to overmix or mash the rice, as you want to maintain some of its texture. The mixture should be sticky and hold its shape when you squeeze a small amount in your hand. If it feels too wet, add another tablespoon of flour; if it feels too dry and crumbly, you can add another whisked egg.
4. Form the Patties: Lightly dampen your hands with water to prevent the mixture from sticking. Scoop about 1/4 cup of the rice mixture and roll it into a ball, then gently flatten it into a patty that is about 3 inches in diameter and 1/2 inch thick. Place the formed patty on a baking sheet lined with parchment paper. Repeat with the remaining mixture, ensuring all patties are a uniform size and thickness for even cooking. For best results, you can chill the formed patties in the refrigerator for 15-20 minutes to help them firm up even more.
5. Heat the Pan: Place a large, heavy-bottomed skillet (cast iron or non-stick works well) over medium-high heat. Add enough vegetable oil to generously coat the bottom of the pan, about 3-4 tablespoons. Allow the oil to get hot. You’ll know it’s ready when it begins to shimmer, or when a tiny crumb of the rice mixture dropped in sizzles immediately.
6. Fry to Golden Perfection: Carefully place the patties in the hot oil, ensuring you do not overcrowd the pan. Work in batches if necessary. Overcrowding will lower the oil’s temperature, causing the patties to steam rather than fry, resulting in a soggy finish.
7. Cook and Flip: Fry the patties for 3-5 minutes per side, undisturbed. Let them form a deep golden-brown crust before attempting to flip them. Once the first side is beautifully browned and crispy, use a thin spatula to carefully flip them over. Cook for another 3-5 minutes on the second side until it matches the first.
8. Drain and Serve: Once both sides are golden and crisp, remove the patties from the skillet and place them on a wire cooling rack set over a baking sheet. This allows air to circulate around the entire patty, keeping the bottom from getting soggy. Avoid placing them on paper towels, as this can trap steam. Sprinkle with a tiny pinch of extra salt and some fresh chives while they are still hot. Serve immediately while warm and at their crispiest.