Season the proteins: toss the chicken with a pinch of salt and a pinch of the white pepper. Pat the shrimp very dry with paper towels and season the same way. Dry shrimp sear; wet shrimp steam and turn rubbery.
Build the aromatic base: heat a wok or large heavy skillet over medium-high heat until hot. Add 2 tablespoons of the oil and swirl. Add the shallots and cook, stirring often, for 2 to 3 minutes until soft and starting to turn golden at the edges. Add the garlic, chilies, and toasted shrimp paste. Stir for 30 to 45 seconds, breaking the paste into the oil, until deeply savory and the garlic loses its raw edge.
Cook the chicken and shrimp: push the aromatics to the sides and add the chicken in a single layer. Let it sit for 1 minute to take on color, then stir-fry for 2 to 3 minutes until just cooked through. Add the shrimp and stir-fry for 1 to 2 minutes, just until pink and curled. Move everything to a plate, leaving the flavored oil behind.
Fry the rice: add the remaining 1 tablespoon oil to the wok and raise the heat to high. Add the cold rice and spread it into an even layer. Leave it alone for 60 to 90 seconds so the bottom grains fry and pick up a little chew, then toss and spread again. Repeat once more. The rice should look dry, separate, and lightly glossy, with a few toasted edges.
Sauce and bring it together: drizzle the kecap manis, light soy sauce, and fish sauce (if using) around the edge of the wok so they sizzle on contact, then toss until every grain turns an even, deep brown. Return the chicken, shrimp, and any juices to the wok. Add the cabbage and scallions and toss for 1 minute, just until the cabbage wilts but keeps some crunch. Taste and add another teaspoon of kecap manis for sweetness and color, or a pinch of salt if needed. Finish with the remaining white pepper.
Fry the eggs and serve: in a separate nonstick skillet, fry the eggs in a thin film of oil over medium-high heat until the whites set and the edges turn lacy and crisp, about 2 minutes, keeping the yolks runny. Divide the rice among warm plates, top each with a fried egg, and arrange cucumber, tomato, crackers, crispy shallots, extra chilies, and lime wedges around the edges.