In a large pot of boiling, salted water, cook the noodles according to package instructions (4 to 8 minutes, depending on thickness). Drain, rinse under cold water and transfer to a large bowl.
Meanwhile, in a small, heatproof bowl, combine the scallions, garlic, ginger, 1 tsp. salt and pepper to taste. In a large skillet, heat 3 tbsp. vegetable oil. Carefully mix the hot oil into the scallion mixture; reserve the skillet. Toss 1 tbsp. of the scallion oil with the noodles so they dont stick together. Set aside the remaining scallion oil.
Add 1 tbsp. vegetable oil to the skillet and heat over medium-high heat. Add the shrimp and season with salt and pepper; cook for 1 minute. Add the carrots and bell pepper and cook, tossing occasionally, until the shrimp is pink and just cooked through, 1 to 2 minutes. Transfer the shrimp to the noodles.
Heat the remaining 1 tbsp. vegetable oil in the skillet. Add the broccoli rabe and season with salt and pepper. Cook until the leaves are wilted and the stems are crisp-tender, about 2 minutes. Add to the noodles.
Toss the stir-fry with the reserved scallion oil until well combined. Serve hot.