Preheat the oven to 425 degrees F (220 degrees C). Line a rimmed baking sheet with aluminum foil.
Combine onion, bell pepper, mushrooms, green beans, and 1 tablespoon sesame oil; toss until well combined. Spread vegetables out on the prepared baking sheet.
Bake in the preheated oven for 15 minutes, turning vegetables after 8 minutes.
Heat remaining 1 1/2 tablespoons sesame oil in a wok over medium-high heat. Stir in rice vinegar and chili-garlic sauce. Add chicken, minced garlic, and ginger. Stir-fry for 5 minutes. Mix in roasted vegetables. Sprinkle with bagel seasoning before serving.
