Season the chicken leg quarters evenly with salt.
Heat the vegetable oil in a Dutch oven over medium-high heat.
Add the chicken and brown on all sides for about 10 minutes, until deeply golden. The chicken does not need to be fully cooked at this stage.
Add the celery, green onions, garlic, poblano, and carrots. Cook for 3 to 5 minutes until softened and fragrant.
Add the bay leaves, red beans, wild rice, and water. Stir well to combine.
Bring the soup to a boil, then reduce the heat to low. Cover and simmer for 40 to 50 minutes, or until the chicken is tender and the wild rice is cooked.
Remove the chicken from the pot and let it cool slightly. Remove the meat from the bones, shred, and return the chicken to the soup. Discard the bones and bay leaves.
To make the corn roux, melt the butter in a small sauté pan over medium heat.
Whisk in the cornmeal and cook for 2 to 3 minutes, stirring constantly until lightly toasted and fragrant.
Slowly stir the corn roux into the soup until fully incorporated.
Season with salt, garlic powder, and black pepper. Adjust to taste.
Simmer for an additional 5 to 10 minutes until the soup thickens to your desired consistency.
Serve hot.