Dice the onion, celery, red bell pepper, and tomato. Mince the garlic and thinly slice the chicken. Set them aside separately.
Add the oil to a pot over medium-high heat. Once hot, add the chicken and spread it out into one layer. Season with 1 tbsp of Cajun seasoning and stir to combine.
Cook for 4-5 minutes until golden and cooked through. Transfer to a plate and set aside.
Drop the heat to low and add the butter to the pot. Add the onion, celery, and bell peppers and cook until tender, approximately 5 minutes. Add the minced garlic and remaining cajun seasoning and sauté for 30-60 more seconds until fragrant. Add the tomatoes and saute for 2-3 minutes.
Add the chicken broth and tomato paste. Stir to incorporate, then let the mixture come to a low boil. When liquid begins to boil, reduce heat to medium-low and simmer for 10-15 minutes.
Add the cooked chicken and heavy cream. Let everything simmer and meld for 3-5 minutes. Taste and adjust seasoning as needed.
Portion soup into serving bowls and garnish with chopped green onions if desired. Serve warm.