Heat the sesame oil and peanut oil in a large skillet or wok over medium-high heat. Add the onion and stir-fry for 4-5 minutes. Add the garlic and cook for 30 more seconds. Add the carrots, bell pepper, broccoli florets, celery, and baby corn, and stir-fry until the vegetables begin to soften, 7-8 minutes. Add the jackfruit and cook until thoroughly heated.
Meanwhile, mix all the stir-fry sauce ingredients together, and slowly drizzle the sauce into the stir fry, stirring constantly. Continue cooking until the sauce thickens and coats all the vegetables and jackfruit.
Mix all the peanut sauce ingredients (except the lime juice) together in a small saucepan over low heat and heat until the brown sugar dissolves, 3-4 minutes. Remove from heat and stir in the lime juice.
Plate each serving of stir fry, then add desired amount of peanut sauce and garnish with sliced green onions, peanuts, and sriracha or chili sauce. Serve with rice.