Use cold rice for the best texture. Break up any large clumps with clean hands or a spoon before you start cooking. Stir together the kecap manis, soy sauce, and sambal oelek in a small bowl.
Heat 1 tablespoon of the oil in a large wok or wide skillet over medium-high heat. Add the chicken and cook, stirring often, until browned and cooked through, about 4 to 5 minutes. Transfer the chicken to a clean plate.
Add the remaining 1 tablespoon oil to the pan. Add the shallot and cook for about 1 minute until softened. Stir in the garlic and optional shrimp paste; cook for 20 to 30 seconds, just until fragrant.
Push the aromatics to one side of the pan. Pour in the beaten eggs and scramble them until softly set, about 1 minute. Mix the eggs with the aromatics.
Add the cold rice and peas and carrots. Stir-fry, pressing and tossing the rice to separate the grains, until hot and lightly toasted in spots, about 3 to 4 minutes.
Return the cooked chicken and any juices to the pan. Pour in the kecap manis mixture, add the scallions and pepper, and toss constantly until the rice is evenly brown and glossy, about 1 to 2 minutes. Taste and add a little more sambal if desired.
Serve right away with cucumber slices, tomato wedges, optional crispy fried shallots, and lime wedges.