Bring chicken stock, ham hocks, and bay leaves to a boil in a large stockpot.

Reduce heat, cover, and simmer over low heat.

Heat 1 1/4 cups of vegetable oil in a very large, deep skillet until shimmering.

Season the chicken quarters with 1/4 cup of Jan's Spice Mix.

Sear the chicken in batches over moderate heat until deeply browned, about 5 minutes per side. Transfer to a plate.

Add the seared chicken to the simmering stock, cover, and simmer until cooked through (30 minutes for breasts, 50 for legs).

Transfer cooked chicken to a bowl.

Continue simmering the ham hocks until tender, about 10 minutes longer, then transfer to the bowl.

Skim the fat from the stock and keep warm.

Pour the oil from the deep skillet into a large cast-iron skillet and heat.

Whisk in the flour and cook over moderately high heat, whisking constantly, until a deep brown roux forms (about 8 minutes).

Scrape the roux into a heatproof bowl.

Heat the remaining 2 tablespoons of oil in the very large, deep skillet.

Add celery and onions and cook over moderately low heat, stirring occasionally, until slightly softened (about 12 minutes).

Add jalapenos, bell peppers, and poblanos and cook, stirring occasionally, until softened (about 10 minutes).

Add okra, garlic, and the remaining 1/4 cup of Jan's Spice Mix and cook over moderate heat, stirring, until fragrant (about 5 minutes).

Add the chopped tomatoes and simmer until most of the liquid has evaporated (about 5 minutes).

Whisk the roux into the warm stock and simmer over low heat, whisking until smooth.

Stir in the cooked vegetables and simmer for 30 minutes, skimming the fat from the surface of the gumbo occasionally.

Pull the meat from the chicken and ham hocks and cut it into 1-inch pieces.

Add the meat to the gumbo along with the andouille sausage and simmer for 10 minutes.

Add the scallions, whisk in the file powder, and simmer for 5 minutes.

Season with salt and serve.