1. Preheat a wok or large frying pan over high heat until it just begins to smoke. Add 1 tablespoon of oil.
2. Saute onion and carrot for 2 minutes until onion starts to soften.
3. Stir in garlic and sambal oelek and cook for 1 more minute until aromatic.
Combine the peas, ham, and rice in the pan and stir-fry for 2-3 minutes until the rice is warmed through. Drizzle in the kecap manis, stir well, and cover to maintain warmth.
In a large non-stick frying pan over medium heat, heat the remaining oil. Crack the eggs into the pan one at a time. Cook the eggs for 5 minutes, tilting the pan and spooning some hot oil over the yolks occasionally, until they reach your preferred level of doneness.
Portion out the rice mixture and cucumber into serving dishes. Place a fried egg on top of each dish. Finish by drizzling extra kecap manis over the dish before serving.