I heat the oil in my Dutch oven over medium heat, then whisk in the flour until it's completely smooth. From there, I stir constantly for about 20 to 25 minutes as it slowly darkens. I'm looking for a deep peanut-butter to chocolate brown color, since that's what gives creole gumbo its signature depth.
Once the roux hits that color, I immediately add the onion, bell pepper, and celery to stop it from cooking any further. I stir everything together for about 5 minutes until the vegetables soften slightly. Then I toss in the garlic for just one more minute so it doesn't burn.
In a separate skillet, I brown the sliced andouille sausage until it gets some color on the edges, then set it aside. I do the same with the chicken pieces, browning them lightly since they'll finish cooking in the pot later. This step builds extra flavor before everything joins the gumbo.
Back in the big pot, I pour in the chicken stock a little at a time, whisking so the roux dissolves smoothly instead of clumping. I add the diced tomatoes, bay leaves, thyme, and creole seasoning, then bring the whole thing to a gentle boil before dropping the heat down.
I add the browned chicken and sausage back into the pot and let it all simmer uncovered for about an hour, stirring occasionally. This is where the flavors really deepen and the gumbo starts smelling like something special.
In the last 5 to 7 minutes, I stir in the shrimp so they cook gently in the hot broth without turning tough. Once they're pink and opaque, I remove the bay leaves, stir in the parsley, and it's ready to ladle over rice.