Bring a small pot of water to a boil. Add the precooked udon noodles and warm for 1 minute, or according to the package instructions. Drain well.
Meanwhile, heat the sesame oil in a small skillet over medium-low heat. Add the shallot and cook, stirring, until softened, about 1 minute.
Add the garlic and ginger and cook until fragrant, about 30 seconds. Stir in the light and dark soy sauces, sriracha, and honey. Cook, stirring, until the sauce is glossy and slightly thickened, about 1 minute.
Add the warmed noodles and toss until thoroughly coated. Stir in the sesame seeds and green onion.
Divide among bowls and finish with a drizzle of chili oil, if desired.