Preheat a large, heavy-bottomed stockpot over medium heat.
Pour in the vegetable oil and, when it’s smoking hot, gradually and carefully whisk in the flour, forming a “roux.” Continue stirring the roux, whisking constantly until it begins to deepen in colour. Be careful, it’s very hot! This browning process weakens the roux’s ability to thicken the gumbo, but it also adds lots of authentic, distinctive flavour.
After 5 minutes or so, when the roux is a deep golden brown, add the Holy Trinity of Louisiana cooking: the onion, green pepper and celery. Add the garlic cloves and stir them for a few minutes until they’ve softened. Add the chicken broth and stir until it thickens. Add the sausage, shrimp, tomatoes, okra, herbs and spices. Taste and season with salt.
Simmer until the sausages and shrimp are cooked through, about 10 minutes. Add the green onions. Serve immediately.