RICE:

• 2 tablespoons butter
• ½ medium onion, cut in 1/2-inch dice (about 3/4 cup)
• 1 medium carrot, peeled, cut in 1/4-inch dice (about 3/4 cup)
• 2 to 3 slices deli ham, cut into 1/2-inch pieces
• 2 cups cooked medium-grain rice, preferably day-old or cooked a little dry
• 2 tablespoons ketchup, plus more for serving
• 1 teaspoon soy sauce
• ¼ cup frozen peas
• 1 tablespoon chicken stock or dashi (optional)
•  Salt and pepper
•  Canola or safflower oil, or other neutral oil

OMELETTE:

• 1 teaspoon canola or safflower oil, or other neutral oil
• 4 eggs
• 1 teaspoon dashi or water
•  Salt and pepper

1. Make the rice: Heat a large skillet over medium-high. Add 1 tablespoon butter, and then onion and carrot. Cook, stirring, until onion is translucent and a little browned at the edges, about 3 minutes. Add ham and cook, stirring, until it begins to brown, about 30 seconds.
2. Add remaining 1 tablespoon butter, and then rice, breaking it up with a wooden spoon or long chopsticks. Adjust heat to medium and cook until the grains are glossy, 1 to 2 minutes. Stir in ketchup and soy sauce, and cook, stirring, another 30 seconds or so to caramelize. Stir in peas to heat through, and deglaze the pan with dashi or chicken stock. Remove from heat and season to taste with salt and pepper.
3. To make a perfect mound of rice on each plate, grease a small bowl with canola or safflower oil and pack 1 cup of the rice. Invert this over a plate and remove the bowl. Repeat with the other half of the rice on a second plate.
4. Make the omelet: In a small (6- or 7-inch) nonstick skillet (or a well-seasoned carbon steel omelet pan), heat 1/2 teaspoon oil, or just enough to coat the pan, over medium-high. Beat 2 eggs with 1/2 teaspoon dashi or water, until yolks and whites are completely blended. Season with salt and pepper.
5. Pour the egg mixture into the heated pan. Shake and swirl the pan over the heat, stirring constantly with chopsticks or a fork as the eggs cook. When lots of small curds have formed and the eggs are custardy, about 30 seconds, let cook undisturbed until nearly set, about 30 seconds. Run a butter knife or small spatula around the edge of the omelet, and tap the pan firmly against the stove to release the omelet. Turn the omelet out onto the rice, custardy side down. Use a clean dish towel or paper towel to push the edges under the rice.
6. Repeat with the other 2 eggs for the second omelet. Dress the omelets with a zigzag of ketchup (or a cute design if you’ve got a steady hand), and serve.

Source: Cooking NY Times