Preheat Blackstone griddle to medium heat. Drizzle vegetable oil then add the celery, onions, green peppers, chicken, and sausage. Sauté for 7-10 minutes until the vegetables are tender and the chicken is fully cooked.
Add the green onions, garlic, and rice to the griddle season with Cajun seasoning to taste. Stir and cook for another 3 minutes.
Pour the tomato paste and chicken stock over the jambalaya then mix with spatulas until completely mixed. Remove from the griddle and top with green onions. Serve immediately.