Toss the shrimp with the salt and set aside. Mix the kecap manis, soy sauce, oyster sauce and white pepper in a small bowl.
Cook the noodles in boiling water for 1 minute less than the package says. Drain, rinse briefly under cold water, and toss with 1 tsp of the oil so they do not clump.
Heat a wok or large skillet over high heat. Add 1 tbsp oil and fry two eggs sunny side up until the edges are crisp and the yolks still soft, about 2 minutes. Slide them onto a plate.
Add the remaining 1 tbsp oil to the pan. Fry the shallots, garlic and chilies for 30 seconds until fragrant. Add the shrimp in one layer and cook 1 minute per side, until pink. Do not cook them fully, they finish in the sauce.
Add the choy sum stems and tomato and stir fry for 1 minute. Add the noodles and the sauce mix and toss constantly for 1 to 2 minutes, until the noodles are glossy and slightly caramelized in spots. Add the choy sum leaves for the last 20 seconds.
Divide between two bowls, top each with a fried egg and fried shallots, and serve with lime wedges.