Bring 3 quarts water to a boil in a large saucepan for cooking the noodles.
Mix the shrimp and 1/2 teaspoon curry powder in a small bowl and set it aside. Mix the garlic and remaining 2 teaspoons curry powder together in another bowl and set it aside. Mix the broth, soy sauce, and mirin together in a third bowl and set it aside.
Add 1 teaspoon salt and the noodles to the boiling water, stir to separate, and boil until tender, about 1 minute. Drain thoroughly and set the noodles aside.
Meanwhile, heat 2 teaspoons oil in a 12-inch nonstick skillet over medium-high heat until shimmering but not smoking. Add the shrimp and cook until slightly browned, about 45 seconds. Turn the shrimp with tongs and continue to cook for another 45 seconds. Remove the shrimp from the pan and set them aside in bowl.
Reduce the heat to medium and add the remaining 2 teaspoons oil. Add the garlic and curry powder mixture and cook until fragrant, about 30 seconds. Add the shallots and stir-fry until they begin to soften, about 30 seconds. Add the bell pepper and stir-fry until crisp-tender, about 1 1/2 minutes. Add the softened noodles, shrimp, broth mixture, and bean sprouts and toss until the ingredients are combined and the noodles heated through, about 1 minute. Serve immediately.