Start by giving your chicken thighs a flavor-packed coat. Season them with kosher salt, black pepper, white pepper, cayenne, chili powder, and paprika. Then toss the pieces in all-purpose flour, ensuring each piece has a light, even coating. This creates a crispy base for your chicken and helps thicken the sauce later.
Heat the vegetable oil in a Dutch oven over medium-high heat. Once the oil’s shimmering, place the chicken thighs in the pot, skin side down (if using skin-on). Brown the chicken pieces for 3-4 minutes per side, developing a golden, flavorful crust. Set them aside on a plate once seared.
Don’t drain that flavorful oil! Reduce the heat to medium. Stir the leftover flour into the oil and chicken drippings, creating a roux. Continuously stir for about 5 minutes to develop a medium-brown color. The roux is key to creating the sauce’s deep, nutty flavor, so don’t rush this part!
Toss in the diced onion, celery, poblano pepper, and minced garlic. Sauté them in the roux until softened and fragrant, about 5 minutes. This forms the aromatic foundation of your sauce.
Pour in the fresh and canned tomatoes, followed by the chicken broth. Add the thyme, bay leaves, and a few dashes of hot sauce to taste. Stir everything together and bring to a simmer. This sauce will bloom with flavor as it cooks!
Return the browned chicken pieces to the pot, nestling them into the simmering sauce. Cover the pot and cook on low heat for about 45 minutes. The sauce will thicken and cling to the chicken, and the flavors will meld beautifully.