Place noodles in a large bowl and cover with hot water. Set aside until noodles are softened, about 15 minutes. Drain and rinse thoroughly.
Roll tofu in cornstarch. Heat 3 tablespoons oil in a pan over medium-high heat. Fry tofu until crisp, about 5 minutes.
Combine 1 teaspoon oil, curry paste, garlic, and ginger in another pan over medium heat. Cook and stir until fragrant, about 2 minutes. Add vegetable broth and coconut milk slowly. Cook, stirring often, until sauce is heated through, about 10 minutes.
Combine noodles, tofu, curry sauce, and green onion in each serving bowl.