In a small bowl, whisk together ingredients for the sauce. Set aside.
In a separate small bowl, whisk together ingredients for the slurry. Set aside.
Bring a pot of water to a boil and cook noodles according to the directions on the package. Drain and remove from heat. Set aside.
Heat sesame oil in a wok or nonstick skillet over medium-high heat. Once the oil is shimmering, add peppers, shallots, onion, and carrots. Cook the vegetables, stirring occasionally, until softened, about 8 minutes.
Stir in ginger and garlic, cooking for another minute or 2 until fragrant.
Push the vegetables over to the side and add the sauce and slurry to the empty side. Cook until the sauce is thickened, about 2 minutes, then stir in vegetables.
Stir in noodles and toss until the whole mixture is coated evenly.
Taste and season with salt and pepper as desired. Garnish with sliced scallions and serve immediately.