Finely chop the onion, bell peppers, celery, green onions, and parsley. Mince the garlic. Season the chicken thighs generously with cajun seasoning.
Heat a large skillet over medium-high heat and add the avocado oil. Sear the seasoned chicken thighs in batches for about 3–5 minutes on each side until browned.
In the same skillet, lower the heat to medium and melt the butter. Whisk in flour until combined and stir constantly for about 10–15 minutes until it reaches a medium brown color.
Add chopped onions, bell peppers, celery, and half of the green onions to the roux mixture. Sauté for about ten minutes until softened, then stir in minced garlic and cook for an additional minute.
Slowly whisk in warmed chicken broth until fully incorporated. Stir in browning sauce before returning seared chicken back into the pan. Let simmer on low heat for about thirty minutes.
Remove cooked chicken thighs from the pot and chop into bite-sized pieces before adding back into the stew along with chopped parsley. Adjust seasoning with more cajun spice if desired.
Scoop portions over fluffy white rice topped with remaining green onions.