If using chicken breast, butterfly or cut in half horizontally to make it thinner and cut down on cooking time.
Season chicken lightly with salt and black pepper.
Heat 3 tablespoons vegetable oil in a cast iron skillet. Cook chicken until lightly browned, remove from heat, and set aside to cool. It will finish cooking in the hot gumbo broth.
Place the andouille sausage in the same skillet flat, and cook until lightly charred. (I do this because I like a little charring on the sausage, but you can skip this step).
Using a Dutch oven on medium to low heat, heat 1 cup vegetable oil. Be very careful not to scorch or burn the oil. Once oil is hot, slowly whisk in 1 cup plus 2 tablespoons flour.
Continue whisking or stirring flour and oil mixture until your desired color. This is the roux and is the most important part of making a good pot of gumbo. I prefer a very dark chocolate color roux, which requires constant stirring for about 35 to 40 minutes.
Once the roux has reached the color you prefer, stir in onions, celery, and bell peppers (the Trinity). Add 2 tablespoons Cajun spices. It will be thick; continue to stir for 10 to 12 minutes until vegetables begin to soften.
Slowly pour in broth; pour a little, stir a little, and keep repeating until all broth has been added to the pot.
Turn heat down to medium-low, add 2 bay leaves and cover, and allow to simmer for 10 minutes. Stir and taste for flavor; add 1 tablespoon more Cajun spice if needed.
Meanwhile, pull chicken into shreds or cut chicken into bite-sized chunks. Add chicken to the pot, cover and simmer for 5 minutes.
Stir in andouille sausage; cover and simmer for 5 minutes.
Add shrimp and crawfish tails to the pot. Stir, cover, and simmer until shrimp is opaque, about 3 minutes.
Turn heat off and allow gumbo to sit, covered, for 10 minutes. Remove bay leaves and serve with a side of rice.
