Soak noodles: Bring 8 cups water to a boil in a large pot. Remove pot from heat and add rice noodles. Stir well so they don’t stick, then let soak, stirring frequently, until soft and al dente. Drain and rinse well with cold water. (If not using the noodles right away, toss them with a little oil to prevent sticking.)
In a medium bowl, whisk together oyster sauce, soy sauce, fish sauce, sriracha, brown sugar and ¼ cup of the water.
In small bowl, beat eggs with 1/8 tsp salt.
Heat 1 Tbsp of oil in a large (12-inch) nonstick skillet or wok over medium-high heat until shimmering. Add shrimp and sprinkle with 1/8 tsp salt; cook, tossing occasionally, until shrimp are opaque and just cooked through, about 2 mins. Transfer shrimp to large bowl.
Add 1 Tbsp of oil to skillet; add eggs and scramble until cooked through. Transfer eggs to bowl with shrimp.
Add broccoli to pan along with 1/8 tsp salt and remaining ½ cup water. Cover and steam until cooked through, about 2 mins. Transfer broccoli to bowl with shrimp and eggs. Discard excess water from pan and wipe it clean.
Return pan to stove, increase heat to high, and add remaining 3 Tbsp oil. When oil is shimmering, add light scallions and garlic and cook, stirring constantly, until fragrant, about 1 min.
Add noodles and sauce and toss until noodles absorb sauce and are tender, 3 to 5 mins. If noodles remain a bit tough, add 2 Tbsp water and continue to toss and cook until tender.
Add shrimp, eggs, broccoli, dark scallions, basil and lime juice, and toss until heated through. Taste and adjust seasoning if necessary. Serve immediately with lime wedges, if desired.