Make a turkey stock by placing the carcass in a large stockpot. Add enough water to cover, bring to a boil, then reduce the heat to low and simmer for 2 hours. Strain the stock.
Cut the andouille into bite-sized pieces.
Dice the onion, bell pepper, and celery.
In a large pot, add the flour and oil, and stir over medium heat for 20-30 minutes to make a roux the color of chocolate. The roux must be stirred continuously to prevent burning.
Once the roux is formed, stir in the onion, bell pepper, celery, and garlic and brown for 5 minutes, stirring frequently.
Add the andouille and cook for another 5 minutes, stirring frequently.
Add the turkey stock and stir until the roux is mixed well with the water. Bring to a boil, then reduce heat and simmer for 45 minutes.
Add the turkey meat and continue simmering for another 20 minutes. Season to taste.
Serve with rice and french bread.