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Step 1
Heat oil over medium high heat in a cast iron or heavy bottomed Dutch oven.
Step 2
Season chicken on both sides with the salt, pepper and Cajun seasoning. Cooking in batches, brown the chicken on all sides; remove and set aside.
Step 3
Add oil to the pan drippings, if needed, to equal 1/2 cup total and heat over medium high heat, slowly whisking in the flour a little at a time.
Step 4
Cook until flour is incorporated, and no lumps remain, stirring regularly, for 4 minutes, scraping up the fond from the bottom.
Step 5
Add the onion, bell pepper and celery and cook for 3 minutes, then begin adding in warmed water or broth, a cup at a time, constantly whisking it in until well incorporated and blended in.
Step 6
Bring to a boil, reduce heat to low simmer, return the chicken to the pot and simmer uncovered for 1 hour.
Step 7
Add the chopped garlic and hot sauce and let cook another 30 minutes. Taste for seasonings and add additional salt, pepper and Creole or Cajun seasoning as needed.
Step 8
To thicken the gravy, skim excess fat from the top of the drippings and discard.
Step 9
Prepare a slurry of 2 tablespoons of cornstarch mixed with just enough water to dissolve.
Step 10
Remove the chicken from the pot and set aside. Bring drippings up to a boil, slowly stirring in the slurry. Boil, stirring constantly until mixture is thickened to desired consistency.
Step 11
Serve over hot rice or mashed potatoes, with a non-starchy green vegetable such as broccoli, a salad, green beans or Brussels sprouts.