Add the diced potatoes to a saucepan and fill it with water, about an inch above the potatoes. Add about 1 1/2 teaspoons kosher salt to the water and bring it to boil. Let the potatoes simmer for an additional 5 to 7 minutes, until they are fork tender. Drain the potatoes.
Heat a wok or large sauté pan with 2 tablespoons of oil over medium-high heat. Add the onions and cook them for 2 to 3 minutes, until they start to soften. Add the garlic, ginger, and chiles (if using), and stir with the onions until they are fragrant, about 15 to 20 seconds.
Next, add the carrots, broccoli, and 1/2 teaspoon kosher salt. If the wok or sauté pan is very dry, add 2 to 3 tablespoons of water. This will keep the vegetables from burning. Cover the wok or pan and cook for about 2 to 3 minutes.
Add the cooked potatoes, rice, scallions, yellow curry powder, and soy sauce to the wok or pan. Stir until the rice takes on a nice yellow color. Taste the fried rice and adjust the seasoning to your taste.
In a separate large nonstick pan or skillet, add the remaining 1/2 tablespoon of oil over medium heat. Fry up the 4 eggs. It takes me about 4 to 5 minutes to cook the sunny side up eggs.
Serve the rice in 4 bowls and add a fried egg in each bowl. Garnish with additional sliced scallions, red pepper flakes, and chili oil, if you like.